I'm in Michigan, so similar weather. I don't really notice too much change in the Winter months, maybe a bit of slowing in the number that move out, but parsing through many years of data, I don't see any identifiable patterns of slowing rentals when it gets cold and blustery. 0
Having said that, I have been seeing extremely strong rent up in the past 3 months. I recently did a 44% expansion of a site, got occupancy in the second half of July, and penciled in ~11 months for rent up (to 85% units); I got there in 45 days instead. Now sitting at 92% at just over 3 months of time.
I never offer discounts. Anecdotally, the tenants I seem to have the most problems with are those that I "enticed" with deals to move in. I feel that someone shopping purely on price, also has a larger propensity to have other issues that may make them a less than ideal tenant. I pitch myself as having a much better value than anybody else (lighting, security fence, 24/7 access, flexible office hours, free lock/keys, etc...) It also doesn't hurt that despite being in a very tertiary and saturated market, it's hot right now and I'm the only one with space available.
I've raised street prices 3-4 times so far this year, and as the cold weather gets here, I will review my current tenant accounts, and start bumping those prices up as well.