Yes you should have a pump and if you have only one, it should be portable, so you’ll have it when you need it. Something that has a hose, so you are pushing with as much of your weight as necessary against the ground, not a pump that requires you to push with arm strength while holding the other end with your other hand which is probably connected to your weaker arm. And it should have a gauge.
Just my opinion, many prefer a floor pump at home and CO2 on the road…
Everyone’s different, but snow bothers my eyes more than my face, so glasses, preferably clear lens, or goggles would be a priority over face mask for me, but if it’s really coming down, you need both. If it’s really coming down, I’m trying not to ride my bicycle. :p