I'm ready to make a few of these for our doors and our floors (I swear there is a draft where our floor meets the wall!).
Are you in a house or apartment?
If its a house what floor is it on?
There could be several reasons for a draft, many of which I am currently stumbling through trying to solve. Two big causes for draftiness in a house are attics and basements. Air sealing each of these as best you can will reduce draftiness in a house significantly. Blocking and sealing the rim joists in the basement can help fix a cold floor, especially if it feels drafty near the wall. I recently air sealed my attic and insulated, and my wife commented on how the floor feels warmer. I assume this is because there is less air moving upward cooling off the floor (but who knows?).
Other sources are doors and windows (which is what you are attacking). If its from a door inspect the weather stripping. Replace/add as needed. Another check would be to remove the trim and investigate if there is any insulation between the door frame and the studs. If not, an easy to to remedy this is the spray in some door and window expanding foam. Remove trim and apply spray foam to windows as well. This will help with the drafts that are caused due to air gaps.
If you are in an apartment and can't do any of the above. Any material that does not allow air flow will work. Foam board cut to shape, dense pack cotton or wool, or cellulose insulation (you could make a bunch of these blocks with cellulose insualion from HD which is 6$ per bale).