Discussions

The plug that is outside home can't turn on the lawn mower. It cant also turn on the hair dryer which I used to test the plug. . could the plug still work in the winter to plug the car ? How may make sure that it would work before winter and really plugging the car?

you have a friend or family member that could help you check the breaker for it in the panel? It might be that simple.

If you plug a hair dryer or any thing electrical in and it doesn't work the outlet is not working

Being an outside outlet there’s a good chance it’s a GFI outlet. There should be two buttons that push in. Thy pushing the one that is raised it may have tripped.  
 
It’s the same outlet as what’s used in bathrooms and areas with humidity.

The GFI reset button you need to press might also not be on that outlet but another one of your outside outlets.

Today, I used a voltage tester and the tester light glows. I also used a plug in night light, which turned on. So seems there is electricity in the plug. Maybe it works only for lower Watts ? Maybe car plug needs less watt in order to work and hair dryer needs more? And the plug still can work and warm up the car?  
By the way, the plug is old and does not have reset button and there is no other outlet outside the house.

none of your theories are right. call an electrician before you burn your house down