Simple car driving game for small kid

I'm seeking a game for my 3+ years old son, who is keen on cars, of course, and likes just driving them in any way. What I need is a game, simulator, with one car, where I can drive freely either on the road or just anywhere, controlled just by arrows, automatic gearbox, no time limit or racing, nothing, just riding as you like.

I have already simulator of Maluch Car: http://www.slunecnice.cz/sw/maluch-sim/ which is just what I need, only the car needs A+Z to change to reverse, which makes it already a bit complicated. I would need the DOWN arrow to do this instead. Remapping is not possible here.

It doesn't have to bee the car though, but it's preferred.

Please no moralizing about kids and computers. We're fine with this.