Are military jackets warm?

Yes. The military operates in all temperatures. Most of the jackets have removable liners, often of different thicknesses, that let you adjust how much warmth you need.

My field jacket was, esp with the liner installed.

The Navy peacoats the Navy issues are about the most worthless piece of junk still being given to recruits.

As for protection from the cold........they are about as worthless as can be.

with the liner in, they can be pretty toasty for most weather conditions.

It really depends on the jacket or coat. My military issue Arctic parka is really warm; so warm that you can't comfortably wear it in weather above 25 degrees. Your lighter weight Cortext type jackets are very light weight and also have a wool liner that can be worn with it and so they are fairly warm. That wool liner can now be worn as an outer garment but they are not waterproof or wind-proof like the outer Cortext jacket is which is what you are referring to probably. With thermal underwear underneath your uniform you could be fairly warm except in the coldest climates on the coldest days where the temperature approaches the low teens.

no