Trentay:
If the ponds are dry enough to drive the tractor on them without getting stuck, a rotary brush cutter (brush hog) would be best for mowing the bullrushes and tules IMHO, and would also mow the vegetation along the roads -- cost $500 to $1200 for a new unit, depending on size and manufacturer, but you may be able to find a good used one. HOWEVER, if you are really concerned about the vegetation choking out the ponds, mowing won't help. They will just come back thicker than before. Burning will have the same effect.
I am aware of two methods for reducing the bullrushes and cattails: (1) rent a mini-excavator, so you can reach out and take out enough material to get most of the roots -- you might have the problem then, of what to do with the material you remove, unless you just pile/spread it on the banks and let nature take it's course; or (2) get someone who really knows what they are doing to deepen and reopen the ponds by blasting -- Wildlife refuges use this method a lot, but it requires someone trained and experienced in the use of explosives to ensure the desired result. It is not recommended if you have buildings with windows or neighbors close who would object /forums/images/graemlins/shocked.gif /forums/images/graemlins/shocked.gif -- the "waste" material gets spread by the explosive in this case /forums/images/graemlins/wink.gif. Your local Fish and Game Department may have someone or be able to recommend a qualified blaster.
With the mini-excavator method - depending on the size of your ponds - you may be able to pile the waste material and create nesting/resting islands in the ponds. Also, since mini-excavators have tracks, rather than tires, they may be able to get around on soft material easier without geting stuck. The specs I have seen often show only 4-6 lbs/sq. in. track pressure. Around here (Central VA), I can rent a mini-excavator for $500-$700 per week.
Good luck.