yeh snow sticking to the wires then going to the ground might ground things, but then I have no idea, water only conduct if it has salt traces. SOem snow belt people may bave to chime in.
With a three acre field and no AC nearby I would use three strands of high tension wire and not even worry about the electric you can add a DC charger to the top strand if you like and let it run best you can. The cable will keep the horses in whether it is electrified or not. One or two zaps early on will suffice for most horses.
High tension cable is dirt cheap, strong safe, a tree can fall on it it just stretches, You cut the tree and it springs back up. You just have to really really really brace the corners. At least 2 foot deep posts in concrete, then angled braces also in concrete. Let posts set up a couple days then you run the cable post to post, with T posts every 20 feet just wacked in the ground. On each run you have this double ended ratchet gadget with a big spring. That ratchets the cable tight like a comealong.
Putting that up will probably be cheaper than the electric cord and it lasts forever. The wire is solid core wire, Picture Barbwire with no barbs.