Look in the winter but avoid the pressure to buy. There are so many variables, it is impossible to define your best strategy. What are you interested in buying? Models later than 2010? 2000? 1990? 1980? Earlier? The risk in purchasing a boat with a failing engine increase as the age increases, but not necessarily. Any purchase you make in the winter will probably be done with an escrow for the sea trial (which is typically done only to verify how the engine runs). I would do that only for a later model boat, after observing the engine and maintenance records, having a survey done, and feeling very comfortable that the engine will be fine. I wouldn't do that for a boat over 20 years old, roughly speaking.
Are you interested in very popular brands such as Catalina, Hunter, Beneteau, etc or are you open to models that you don't see on the market very often. If you want only a Catalina and nothing else, you will undoubtedly find far more on the market as you approach spring. The best boats probably won't be on the market in the winter. Who wants to try to sell their pride and joy when there are very few buyers, and the buyers that are out there are probably expecting a bargain price. The sellers of the boats that you want to see probably will wait until spring to show off their prize.
OTOH, you just might find that prize in an unusual circumstance, so it doesn't hurt to look. I would take the time to look, but patience is a virtue. You can sort out the marina & insurance quickly. There is no reason for those issues to put pressure on you for a purchase.
If you don't know exactly what you want yet, use the winter to scope out a variety of boat brands and models. Decide on your criteria for selection first, then focus on the window of selection within a narrow range for shopping in the spring when there will be more to choose from. We started our search in late March last year and purchased in mid June. We narrowed down to the boat brand and model (actually, that process started earlier) before focusing on the search parameters, based on model year, asking price, and location (from Massachusetts to North Carolina). I ranked 15 boats in my focus group, based only on the advertising. Obviously, I was focused on a very popular model. Then I called as many contacts as I could reach, asked about the boat and scheduled times to make a visit if I was still interested. COVID made it impossible to see as many boats as I would have otherwise. Looking back, there were a lot of boats in my focus group on the market last spring. Far fewer now, I've noticed. The cycle will repeat.
Everything works two ways. More boats on the market … more pressure on Seller. More buyers in the market … more pressure on you to purchase what is available. Fewer buyers in winter … fewer sellers, too, and probably a meager selection. However, you will never know exactly when the right boat for you presents itself.