How do you moisturize after washing your face in winter?

These days, as the weather suddenly got colder, my skin feels tight and dry right after I wash my face.

I'm wondering if I'm washing my face incorrectly, or if I'm just not moisturizing properly. I use a light foam cleanser in the morning, and in the evening, I wash my face with lukewarm water and finish with a foam cleanser. However, just a few minutes after washing, my skin feels tight and dry.

I've heard that in winter, you need to be mindful of the water temperature and amount you use when washing your face, but I'm not sure how to adjust that. I also apply moisturizer, but it absorbs quickly and feels dry, so I'm wondering if I should layer it more.

I've been trying to drink water consistently because I've heard that daily habits can have an impact, but I feel like that's not enough. Maybe it's because I sleep with the heater on, but when I wake up in the morning, my face feels even drier.

I'd like to hear your opinions on how to moisturize right after washing your face in the winter, and what lifestyle habits I should pay attention to that would be helpful.