'99 Forester won't start when it's cold, even after replacing battery, cables, and starter

The car is a little older. We've done a lot of work on it, and it runs fine once it
warms up a little, but it won't start when it's cold in the early mornings--won't
even turn over. This is going to be more of a problem as winter is coming,
but we've replaced the battery (twice, actually) and the terminals/cables. We
recently replaced the starter, but the problem persists. Anyone know what
else could be causing this/a potential solution? Is this a common problem
with this model?