I'm not sure anyone really answered your "treadle" question very well.
The JD product(s) typically have two pedals to activate the forward and reverse on the tranny. They are located quite close to one another and the operator rests his heel on the floor and alternates between pedals as needed. Very intuitive to operate and (for me) less fatigue.
The "treadle" (as found on the 'bota) has a sinlgle pedal with a center pivot. Thus, when the heel pushes the pedal you go backward and when the toe pushes the pedal you go forward. Holding your foot in place on a treadle is hard for me. Maybe not a deal breaker......but I prefer the double pedal as in the JD.
Hope this helps.
Also, if you are concerned about "enough" HP....you could go to the next size JD (3038) which would add 6 HP and more CID to the same tractor size. I'm not sure how much this will change the loader specs (if any) and how much this adds to the cost. Given your slippery yard, I would definately get Ag tires (R1's)