I have owned a snow bike for 4 years and never used wheels under the ski, for loading in a trailer or pickup bed. Yes wheels make the bike easier to maneuver around especially during off season if it stays as a designated snow bike in the shop or garage.
Ladder ratchets into the floor or side walls are my favourite. I also secure the tunnel through the sub frame as well as handle bars.
The ski can easily slide out left or right of you on ply wood or other slippery surfaces, so keep both feet planted and walk the bike up the ramp to load.
When Using my pick up only, I fabricated a bracket out of aluminum for on top of my aluminum tool box, I remove the ski, lift the front of the bike on top of my tool box and run the bolt through the bracket and spindle, then ratchet straps on handle bars and then I can close my tailgate ( short track only on an 8' truck box the tool box still opens for access to tools, Gerry cans etc.)