Does prednisone increase urination?

Yes it can. And keep in mind that prolonged use can cause urinary incontinence. Like when you cough and sneeze, etc. It will subside after you stop taking it.
Check the entire list of side effects for prednisone. It's quite lengthy.

I find that to be true. ESP on higher doses.

Yes, taking prednisone can make your blood sugar levels in your body increase, thus making your more thirsty. Other signs of prednisone use are dry mouth, dehydration and water retention.
Finally, it's not uncommon for you to have an increase in hunger while taking prednisone as well.