Generally agree with many of the comments here about the premise. Didn't have any trouble playing in Edinburgh all year when I was living there, even if it was a bit soggy and we had to race against early sunsets.
I would add though, that there are many aspects of 365 day/year courses that are both seasonal and notable. I often find folks talk about courses as though they only play one way, but the two 365 regions I've lived in leave interesting subtleties to the season you're in.
I grew up in central Texas, and playing there is wildly seasonal. The spring there can be soft and even muddy, but the late summer and winter leaves the ground harder than linksland. When the bermuda is dormant, the lies can be the tightest you'll ever play, hence the Texas Wedge. Learning how to play in different seasons can really make a course have variety beyond topography.
Here in the Bay Area, the seasons couldn't be more obvious. Links-style course directly on the bay (Corica, Metro, Monarch) are excellent in the winter for drainage and temperate-if-rainy, even Scottish, weather. Coastal courses (SF city courses, Sharp Park, Bodega Harbor, Northwood, etc) are excellent in the summer for the cooler, walkable climate. Inland courses (inland Sonoma, Napa, Contra Costa, Alameda, and Santa Clara county courses) are best played in the spring and fall for the most temperate, walkable conditions.