If hot air travels up, why are mountain tops covered in snow?

As the elevation rises, the air thins and less air can bump into it self causing less friction and therefore, less heat.

the hot air passes mountains by and evaporates.

Hot air near earth's surface will rise - especially if surrounded by cooler air. However, the higher in altitude the air is, the thinner it is and thinner air cannot hold heat as well as more dense air, so it cools. At elevations such as the tops of mountains, the air is very thin and has lost lots of its heat. The reason why air is denser at lower altitudes has to do with the pressure of all the air on top of it which is simply caused by gravity.

What happens is the heat rises and as you go up the air gets thinner so I can see the confusion. But there is a simple answer.

First off as pressure drops it is easier for snow to form and also for steam to form so snow will also sublimate directly into vapor.

Second the hot air rises what most people don't realize is that there is a layer in the atmosphere called the thermosphere which is actually quite a bit warmer(near 4000 F actually) but the air up there is so thin that there are so few molecules that you will touch that there is near 0 heat transfer.

Finally with both of these aspects you see that as air gets thinner there is less molecular contact and less heat transfer so you can have snow on mountains even though heat rises.