It's still feasible. I biked to work most days in the winter, and after 5 min or so, I'm plenty warm. I generally avoid going the same day as a snowstorm, but cold weather is pretty easy to adapt to (just wear more layers). Throw on some panniers and you can take off a layer or two if you want (though I prefer to just start colder so I don't need to stop).

Heat is a lot harder though. At a certain point, I just cannot drink water fast enough to keep myself hydrated (I'm in a dry climate), and in more humid weather I can easily overheat. That said, it's fine most of the time, and I only avoid cycling for a few days of the year.

That said, this is for newer cyclists, so I would leave the advice at: "it's feasible, but you'll want to work up to it."