upcruiser, you bring up a valid point.
This has happened to me only once, but boy did it do a mess on my bike, and the rig for that matter...!!
This was at Prudhoe Bay in AK some time at the end of June, 2009
Got cought on a snow storm while going through Atigun pass.
It started with rain, snow, rain....... by the time we made it to Prudhoe Bay it was 22F.
The mud was frozen solid and all components had to be replaced....
However, this was a one time incident.
But this made me not want to have a hitch rack any more..at least not for my overland adventures....
On inclement weather, I usually cover the chain and shifter on my bike with plastic and duct tape...
That's pretty much solve the problem...
On my upright set up, most of the weight is on the rear tire.
The fork is just to secure the bike....
To the OP you should try different set ups, and see what works for you.
I agree that inside is the best place for storage (out of sight, out of mind).
Real state IN my old rig is expensive.
Frank