I have a door similar to this, but it is an external door. There is a lot of cold air coming in from the bottom of this door, and around the perimiter (betweent he door and the frame).
This is a rental house, so I don't want to spend too much fixing this forever, just enough for it to be effective.
How do I prevent cold air from coming into the house?
For the bottom, you need to install a (or replace the existing) door bottom (Yeah, someone was really inventive with that name). The thing goes on the bottom of the door and will fill the gap there.
There are 2 general types, ones with vinyl fins (like this) or ones with short brushes (like this). I personally find the latter work better, though if you have a large gap, the brush type may not be long enough to fill the gap fully, though a gap that large likely means your threshold is improperly sized.
You can get a under the door dual draft stopper that slides under the door like this below. This may work as a temporary fix seeing as your in a rental
For a temporary, low-cost, low-hassle solution, you could just put a towel down in front of the door to block the draft. That's what we always did in my house as a kid.
