Yep, short trips in the cold are the worst for overall efficiency. Short trips tend to have a larger percentage of the trip doing acceleration rather than 'coasting' and this hurts your efficiency. If you are using the climate control, it's similarly working hard to hit a certain temp, but there's less time for it to 'coast' and just maintain that temp once it gets there.
If you want a gut check on whether your short range is due to inefficiency or battery degradation, you could reset your trip computer and get an idea what your mi/kwh is. Anecdotally, I tend to average around 4.0 year-round but in the winter I've logged some trips as long as 10 miles all the way down at 2.5 mi/kwh. Even shorter trips have dipped down to 2.0 (granted, I had no concern for range so that's with no attempt to help the efficiency on my part).
Then if you want to get really nerdy, you could do some additional math to estimate your battery capacity. After a drive where you've measured your trip efficiency, distance, starting and ending battery % you can use the following formula:
(Trip Miles / Trip Efficiency) / (Starting Battery % - Ending Battery %)
For example, for a trip of 40 miles at 3.5 mi/kwh starting at 100% charge and ending at 22%:
(40 / 3.5) / (1 - 0.22)
=11.43 kwh used /.78 % battery used
=14.65 kwh battery capacity at 100%
Be aware that this is a rather rough estimate and can fluctuate. If you do it a few times though, it should point you to the right ballpark of battery capacity.