What kind of herbs are they? Different herbs have different light, temperature, and water needs. Depending on the direction and with extended cloudy days, some of them will find it too dim. But I love the sunny days after snowstorm like this because the slid snowcover reflects the sun and we get extra brightness from all the windows.
Basil in particular will not be able to handle the cold windowsill. Even if weathertight, cold transfers from the window panes. Typically annuals, only basil variety I have been successful in "overwintering" (still sheds leaves and turns into a stump) and having return with new basal growths as lush plant from year to year has been a Thai basil. I do still have one lemon or lime basil barely hanging on.
On the other hand, some borderline winter hardy herbs like Rosemary needs special care and do best in cold but not freezing temperatures -- there are several threads about overwintering Rosemary.
You need to be very careful not to overwater since they will grow slowly if at all.
And it will be normal for perennial herbs to become scraggly-looking and some go into complete dormancy -- dried up-browned leaves, last year's stems die off -- around winter solstice.
Finally, this is time of the year when it's super cold outside and the heat is cranking inside, plummeting the relative humidity. The plants that ARE still green and growing will benefit from daily misting and open containers of water evaporating around them, and you need to be more vigilant for signs of indoor pests.
Post some photos if in doubt of what is causing them to stress.