3L3M3NT
I tow a snowmobile [640#] on a single open trailer [360#], no trailer brakes, just need to go slower as the roads get worse. I do run (4) Blizzaks.
As to trailer brakes, I question if they would help more than hurt on winter roads. If the trailer brakes are set to high[hard] say for a slushy road, and now on a snow packed icy road, might not the trailer brakes lockup and swing the trailer out sideways. I have not pulled a trailer with electric brakes, so my understanding of how they work in the real world might be misguided.
A covered trailer does keep the sled(s) cleaner. 3L3MN3T you may want to rent an enclosed trailer [ U-Haul ] now, to see how it goes. One would need to check it out but, a 5' x 8' V-nose is deeper then 8'. And if, with the sled in back wards, and the tongue weight is OK, then there would be less trailer weight.