Is your asthma controlled beyond a rescue inhaler?

You can try various things like sweat bands and stuff to keep the sweat out of your eyes.

Learn to make friends with your trainer. The key, I think, is to mix it up. Also get a large fan to keep you cool (you heat up fast on a trainer!) and put a small towel over the headset to keep sweat out of it. I'll do ladders one day, intervals another, and just plain old grinding on another. I have TV for the grinding, and I use music for the intervals and ladders.