A lot of stretching work in the arena. General hard work will get him conditioned if you plan on taking lessons. Do rollbacks to get him to work off his hindquarters, work on slowing down really quickly at a canter (rating), do a bunch of circles (not in a row, but every so often). Try doing figure eights, S figures, etc. Get your horse to move off of your leg commands. Get your horse used to neck reining, direct reining, and short reins.

I don’t know how you will be able to do this in the snow unless you have a closed arena…

If you have the extra cash, invest in a show quality barrel racing saddle and breast plate and bridle.