Peroxide is the last thing you should be using. It kills everything - healthy cells, unhealthy cells, etc.. so while it might not get infected, if you are treating daily with peroxide it will never heal.
Betadine is similar, although not as bad as peroxide.
Vaseline is a petroleum based product and is not good to use on wounds at all.
If there are irritants in the horse's daily life then yes, wrapping it is a good thing to do.
As far as treating scratches, mud fever, what have you.. If it really is that bad, don't be afraid to phone the vet. Veterinarians can perscribe a cream or ointment which varies from vet clinic to vet clinic that will generally heal up scratches really quickly.
For home treatment, you'll want to grab fluorhexadine or chlorhexadine (brand name is Hibitane), zinc cream (yes, the white stuff for diaper rashes), gauze pads and more vet wrap. If you don't have tape, duct tape works well and there is a vet wrap type tape as well which stretches and stays put really well, you're also going to need towels/rags.
First of all clean the area gently with a lot of water and some fluorhexadine with a few gauze pads. Scrub very gently if any of the scabs want to come off initially, but otherwise just get the area nice and clean and rinse with plenty of water. Now, towel dry the area and again be careful not to scrub too hard that you cause bleeding. Next, apply the zinc cream liberally to the affected area and cover with gauze pads that serve to hold the zinc cream in place. Next vet wrap the gauze pads on and tape the vet wrap in place. You can leave the wrap on if it hasn't moved or dirt hasn't got up under the bandage for one to two days. Repeat. Now the scabs should come off a lot easier when you clean with the fluorhexadine. Keep doing this until the scabs are gone, and then you can just wipe the cream off with a gaue pad and reapply the wrap and more zinc cream until the skin heals. If this isn't working, you might have to call the vet clinic to get some scratches cream to use instead of the zinc cream.
They say money doesn't buy happiness -- well happiness doesn't buy horses!