Monthly averages only take you so far; it's the extremes you need to worry about. I think you really need to look at daily stats for recent years to have a hope of knowing what you're getting yourself into. For winter travel (not your issue), there's also a tendency for travelers to see an average high temperature and subconsciously interpret that as what they'll experience if they're lucky. In actuality, that high temperature will only show up for a very, very few hours a day in the winter. It will probably be much colder most of the time.
Sometimes, if you look at the fine print, monthly averages are based on periods that ended 10 or more years ago. Given how weird weather has gotten, stale averages can be especially misleading. The last few times I've looked at a climate chart in a city's Wikipedia entry, the time range extended to 2020, which isn't bad. Maybe they've updated them. Previously, I was seeing averages that excluded all years after 2010 or even after 2000; those were pretty useless.