It would take either a lot of coordination or a lot of patience to paint hair with a mouse. I've seen a couple of people do it, though. If you have all the patience in the world, you can do it strand by strand, using the pen tool to make the strands, and then stroking each path you make with a gradually thinning brush.

I wouldn't recommend it, though. It's extremely frustrating and time-consuming.

As Hoofd said, there are tablets you can buy for under $100. Dig deep if you have to, or buy used, but I promise you, it'll be the best investment you ever make.