House? Condo? Apartment? No it is not normal for drafts to be coming in thru the baseboards. This needs to be fixed from the exterior first. The house needs to be sealed, if draft enter, so can bugs, mice, rats, etc. Without more info we cannot begin to offer help.

In traditionally constructed house,s air can circulate through the soffit and crawl space vents and between wall partitions. If there is a pressure differential, and space for air to move under trim or through a switch plate, it will do so.

It’s a 2 story house with an unfinished basement. Looking up into the ceiling of the cold storage area I can see light coming in from a few places around the base of the front door right above. It looks like it’s coming from between the foundation and the framing. I read this can be sealed, but if we do that am I going to have a moisture problem? I’m thinking the reason our cold storage is so dry is because we live in a very dry climate, and because this allows just enough ventilation. If we seal it I’m wondering if we’re going to have the problems I’ve heard about from foundation/basement walls carrying moisture from the outside soil and snow.

if the houses are intentionally built to allow air circulation in the walls, is there anything I can do to account for this in our family room? If we have the heat turned up enough to warm the main room of our house, the bedrooms are stifling. We’ve tried adjusting the vents in a couple of different ways to make it tolerable but this room stays cold, and without carpet it’s much more obvious. This room has the most windows and the cold air return is actually in the next room. I think they considered it one room during construction because it’s two rooms next to each other with a archway in between.

I've seen people use spray foam under base or drywall and in electrical boxes. This might help but your sun exposure, wall insulation and window area probably have larger effects. It doesn't sound like sealing your openings would have an adverse effect. I have a similar situation where I closed in a room with a flat roof and made it my family room. It faces south and doesn't get great ventilation so it's always hotter in summer. The living room on the north side has new wall insulation and is always the coolest so I made it my TV room. Everything will helps somewhat, insulation, better ventilation and shades would help. We had a little cool snap recently and I am surprised how effective my newly installed cellular shades are at insulating the glass areas. Perhaps an HVAC specialist could devise a way to pump more warm air toward your cold room.