I'v never had a problem with my AR's wearing a RA jacket in cold/wet weather, even a clear poncho. There's more important things than the overstated importance on appearance.
I mean, yes, appearance is important, but I'd argue that being highly uncomfortable (even risking your health) is going to affect your game more than some arguably highly subtle notion of whether somebody has a slightly yet imperceptibly lower amount of respect for your because you're wearing something warm that influences them to show greater dissent, which in turn influences other to dissent and destroys your match control.
As a referee with glasses, I'd wear a hat if it so much as looks like raining. although I'd also wear a hat if I have a fairly long day (3-5 games) just to reduce sun fatigue (even mid winter can be well over 20 degrees celsius).
I used to referee at a youth tournament once a year in a particularly cold part of Australia, referees and AR's would be wearing tracksuits and beanies. Just a matter of being much colder than we're used to...and, youth tournament and a full week of weather exposure. So again, it's about what's actually important.
Anyway, Snood, no. Sweatshirt? I'd argue to get yourself a jacket. Gloves, hat, no problem for me as an assessor. Always found it ridiculous that we somehow think that officials aren't allowed to dress appropriately for the weather.
But it's a 'when in Rome' thing, of course. You can disagree with things while still abiding by them!
.
