This week, if they asked, I'd say no.
After a week in which three children were murdered as they did innocent and apparently safe childhood things, the tide of protective fear has risen again. Dread of the sick stranger is every parent's worst nightmare, tapping as it does into primitive fears that go well beyond the rational. According to the charity Kidscape, 95 per cent of us fear abduction and molestation of our child more than anything, and I'm sure I'm not the only mother blindly jerking in the reins in a reaction based more on raw empathy and terror, than on any cool-headed assessment of relative risks and dangers.
All parents perform a constant balancing act between the need to keep children safe, and the need to give them the freedom to grow and develop. The decisions come almost daily - going to the shop, walking to school, biking round to a friend's house, staying home alone - and each step is taken with baited breath. We so want to get the balance right, but there is no right; only a series of gambles that may, or may not, turn out OK.
Even though the figures show us that there is no increase in child murders, and that the likelihood of a child being murdered by a stranger is infinitesimal - between 1983 and 1993, only 57 children under 14 were killed by people they did not know - it doesn't feel safe out there any more.
As a child, one of my favourite play places was a patch of dense scrubland under the railway embankment on the edge of town, but my heart goes cold to think of my own children in such a place.
Why? Because we have all lost our innocence. Child rape, molestation and murder have always been there - unknown, unheeded or brushed away under the carpet - but in this media age we all know every last detail of every hideous incident.
Ten years ago, we had barely woken up to the unspeakable dimensions of child sexual abuse. Now it has become a familiar story. Pornography has gone mainstream. What were once the dark secrets of a minority are now out there for everyone to share.
Society is more mobile. We often don't know who lives next door, and the sick stranger can drive into town at any time, seek out vulnerable victims, and be gone just as fast as motorway burglars can hit distant country houses and be a hundred miles away before the village policeman even gets out his bike.
No matter whether or not the facts actually bear out our fears, if we parents believe it's true, we feel forced to rein in our children.
As an antidote to this pervasive sense of threat, I made myself survey the actions of the children I'd had contact with over the past week. My 10-year-old daughter and a friend, staying in Oxfordshire, had walked over the fields to the village shop and back without incident. My son's friend had come 30 miles by train, alone, to spend the day. My eight-year- old and her friends, aged nine and 11, had played tennis on the village court alongside a busy main road and returned to tell the tale. Every day hundreds and thousands of children live quiet, ordinary lives, going here and there without anything terrible happening to them.
Yet against this is the sense that harassment of children is increasing all the time. "Rationally, I know my child isn't likely to be murdered," said one London mother of two, "but the news stirs up all those other fears about whether they're safe out there, or not."
Her 13-year-old son was recently mugged for his watch at the end of his road, and at the primary school where she is a governor there have been four recent attempts at child-snatching.
Kidscape's assistant director, Jane Kilpatrick, says that if you ask any group of eight or nine-year-olds whether any of them have been approached by strangers, or know anyone who has, at least one or two will raise their hands and tell of encounters at the school gate, or outside a sweet shop, or in the park.
"Parents need to talk to children," she says. "Teaching them about personal safety needs to be as much a part of growing up as teaching them about crossing a road. You need to talk to them every time you go out. Ask them "what if" questions. What if you get lost? What if a stranger tries to talk to you? What if you get separated from your friends? What you are trying to do is to encourage them to think things through, to trust their instincts, and to develop coping strategies."
Many guidelines are obvious. Every child needs to know about not taking lifts from people they don't know and not even going near a car door if someone pulls up to talk to them. They need to know to avoid lonely places, and to stay in twos, or more, and not talk to people they don't know. They must know their own phone numbers, have money to make calls and know how to make an emergency call.
Other things are less obvious. Jane Kilpatrick advises parents to make sure clothes are not visibly labelled with a child's name, otherwise it is all too easy for someone to come up and say, "Hi, Tracy. Haven't seen you for ages. I'm a friend of your Mum's ..." and also says it is important for children to understand that they needn't be polite if they feel under threat, that it's perfectly OK to walk past someone, to not answer questions, or to kick, scream and make a fuss.
Also, she says, don't talk to them about "strangers, because young children don't understand the concept; talk to them about 'people they don't know'.One little boy let a man into the house, who then molested him, because, he said, he wasn't a stranger, he was wearing a suit, just like Daddy."
At the end of all this, though, we still have to face the fact that we can never fully guarantee our children's safety - the children murdered this week, and their families, did everything they should have done to ensure their safety and still the worst happened. All we can ever do is send them out into the world as well-equipped as possible to avoid danger and to handle any dangerous situation that might come their way.
For our own part, we need to keep our parental fears in proportion, and to focus on those dangers we can do something about. Six hundred children a year are killed in road accidents, for example, many preventable, and statistically children are far more threatened by traffic than they are by sinister strangers.
Two days ago, we moved to the city for the summer and as we breasted the Hogsback and sank down into the foul soup that is the London air in summer, I found myself issuing urgent instructions on urban safety to my three children.
The city is full of all kinds of people. You have to stay alert. Watch your backs. Trust your instincts. If people make you feel uncomfortable, avoid eye contact. Walk on. Get away from any situation that feels uncomfortable, and make a big fuss if you can't.
So far, they have been out and about entirely without incident. They can't think what I was talking about. In fact, they feel far safer here than they do in the village, where cars hurtle blindly round every corner and any walk they take is a long hike along lonely lanes.
But at night, as I listen to my son turning in his bed, safe from strangers but coughing and restless from asthma triggered by pollution, I remember that the dangers modern children face come in many different forms. And that, as parents, our duty is to try and do something about them all, the every day and the shocking, as far as we are able.
Kidscape offers a parents' guidance pack on child safety. Send a large sae to Kidscape, 152 Buckingham Palace Road, London SW1W 9TR.