Yes Tires do lose air pressure which means that cold weather decreases air pressure in tires so you might notice in the cold weather that your tires may look a little deflated and sometimes even near flat and it's really very normal for that to happen.
When tires lose air pressure in cold or hot weather it's very normal and all you need to do or can do is constantly check your air pressure in the tires to be sure they're inflated properly.
The reason tires lose air pressure during winter and hot weather is due to changes in the air pressure and it's normal for tires to lose about 1 to 2 lbs of air pressure for every 10 degrees change in the weather temperature.