Where are you located in the world? You can include that general information in your profile so it displays under your stats.
You didn't mention how large your coop is. Can you provide it's dimensions in feet x feet? Pictures of your coop and run would be very helpful.
Here is a link to how I integrated 3 pullets in with an existing flock of 9 birds:
https://www.backyardchickens.com/threads/well-dang-that-was-easy.1281000/
Integrating in the cold weather can be difficult, but 'cold' is a relative term. I would not want to deal with 2 coops in the dead of our winter where we are frequently in single or below zero night time temperatures and everything is frozen.
Quarantine is also important. Do you have a garage you could use to quarantine the new birds? Or some other place you can keep them away from your existing 2 for 3 to 4 weeks before you start the 'look don't touch' phase of the integration? I didn't really have that capability as you can read in my post so I did a pseudo quarantine but everything worked out fine.
Integrating new birds can involve a fair amount of work but if you are up to it, it can certainly be rewarding. I enjoyed it.