I would stop hosing his legs off, moisture is a cause of the problem so you want to keep his legs as dry as possible. I would also stop using Mane and Tail on them since they are probably kind of raw that might be irritating.
Can you work a horse while it has mud fever, as long as they arent lame?
I would give him some time off until you get the scratches (mud fever) under control. You don't want to put any unecessary stretching of the skin in those areas. If you really feel the need to ride, I would keep it to a walk.
Am I doing the right thing?
I would wash his legs really well with betadine scrub. Dry them VERY well.
Then you need to pick up some ointments- Desitin (40% zinc oxide, not the 10% kind), Neosporin/Triple Antibiotic, Cortizone Cream and Athlete's Foot Cream (Tinactin). Mix all of these together in a little gladware/tupperware container and apply that mix to his legs 2x daily (if possible). Put it on liberally.
When you go to re-apply just wipe the old stuff off, don't wash it off. The Desitin will act as a water barrier.
Would MTG work well for the mud fever too (someone told me it would)?
I've heard it does, but the above mix works really well! The ointment sticks to it, whereas the MTG would dry sooner, exposing the scratches again.
Is there anything else I can do to help him?
Just watch it, if it doesn't going away within a week get the vet out to check it because he might need antibiotics.
Should I do some light bareback (walk) in the arena until I feel he is 100% ready to do walk and trot work and such?
Should I do some inhand and lunging up and down hills?
I wouldn't lunge up and down hills, but a bareback walk or inhand trail walking wouldn't hurt.
Hope they heal soon!