10..15 min running the hoe...
I wouldn't call running the backhoe for 10 to 15 minutes "too much". If anything, it's on the short side for getting the fluid warmed up enough to do any good.
It's not uncommon for me to run the backhoe for several hours, basically until it starts getting dark, or I'm about to run out of fuel, whichever comes first.
Probably warming the hydraulics a lot more is when running the snowblower, since that is a constant load. I doubt that even a skilled operator could put that kind of strain on the system with the backhoe. The longest I've run the snowblower continuously is less than two hours, but still.
I'm still curious about why you think it was "too much", and what (if anything) makes you think that there's a problem. Okay, the remote switch isn't working now you say, but that could be air pressure related or for other reasons.
You could power the fans directly to verify their function, one at a time, using either a separate battery or the ones in the SEE,
Also, I wouldn't worry too much about what fuse powers what. Why not replace any or all bad fuses?