Here in Chicago, I’m not sure I’d be able to tell you a Dec 1 from a Jan 1 or pehaps even a Feb 1 with any degree of confidence. At any point, the weather could be exactly the same on any of those dates, and I can’t think of any other external natural cues like foliage or wildlife or whatnot that could reasonably disambiguiate them for me. OK, you have length of day, I suppose, but three weeks before winter solstice vs three weeks after winter solstice, I couldn’t tell you. It’s likely the latter will be colder than the former here, but certainly not a guarantee. For example, last year, December first had a high/low of 34/26; Jan 12, 2021 (about same amount of daylight) was 37/29. Hell, Feb 1 was 34/23. I mean, I could tell if I’m in the city and see Christmas decorations or Valentine’s Day ads, but otherwise, I can’t see how it’s possible to reliably determine a date within 10 days, at least in Chicago. Here I’d be reasonably confident within maybe a month in either directlon, although even then there will be outliers.
With summer, I may have a little more to go on if I’m somewhere with lots of vegetation and crops, as I reasonably know what’s in season when, and how far along various plants are at what time. There I might be able to guess to within two weeks in either direction. With winter, no such cues that I see.