The winch definitely puts a draw on the system. I found a couple of little things that helped out on mine when I first started plowing and had similar problems.
Check the battery water level. Even though the machine was new, couple of months old, the water lever needed significant refilling.
Check the nuts on the three studs to the right of the battery. My ground was rather loose, I could move the able VERY easily.
Put your trickle charger on when you are done plowing.
I did the three things above and it made a big difference. In the short term till I could get an auxiliary battery and all the hardware together.
In case it matters..... 2013 800 full size. I got a smoking deal on a group 24 Exide sealed Marine Battery and put it in the bottom of the tub under the driver seat. I cut a piece of 3/8" plywood over the top so I can still use the storage container for stuff. Still recharge after every plowing event with the trickle charger. No fancy isolator or switches, brackets, mounts, cabling and so on. If I parked and partied then I would invest in additional pieces, my boat and pontoon have the fancy switches and isolators.
Not hating on the Oddessy options but I question the capacity of those little 925's to a good old group 24 or similar size battery. I also believe that dollar per pound and minutes of reserve capacity, the "regular/full" size battery is a better way to go. Space not being an issue.
Du