Some rooms in my house have a pretty bad draft along the edge of the floor, where it meets the outside walls. But I am less than thrilled (to put it mildly) about the prospect of ripping out carpeting and moldings just to seal the draft. Is there any simpler solution out there?
Wait a minute... that may be a very, very bad idea. sorry kacalapy. All I can see is messy carpet after that try. If this carpet is laid on concrete, then the tack strip is fastened with masonry nails, and if installed properly is chiseled over the edge. No way caulking is going to seal the gaps causing the air leaks. If your leaks are that bad, then do the right thing. Take off the baseboards, see if you can access the sills, if not, pull back the carpet, and caulk the gap between the sill plate and the slab. Reinstall the baseboards, then re-stretch the carpet to the tack strip. It sounds like no sill seal foam or sealant was installed under the sills. There is really no quick fix to a problem like this. BTW, foam padding and carpet carry and "R" value of about 3 to 5 max. Carpet is never even considered as an insulating material.
It would serve you much better to tear it out and properly re-seal the bottom plate with fresh acoustical sealant and thicker vapour barrier. Unless you want bigger issues such as mold. You can have insulation slippage etc that can be fixed. I just did the same thing. Other than the time it took it is now properly fixed for a weekends worth of work. Installed higher grade insulation as well.