It's tougher but you'll be fine! I got Jackson in Dec. He had one set of shots and then he got another with me the week I got him. I did not worry about bringing him outside in our yard, at all. Just try to avoid pet stores and dog parks, etc, before vaccines are finished just to be safe. But I've never ever left a dog inside until 5 months old! That just seems.... crazy to me. Imagine a bigger dog and trying to keep them indoors inside. lol. They will be fine, just be precautious of course. Your pup is more likely to pick up diseases at the vet.
But otherwise, good luck! Jackson is a winter baby, he loves the snow etc because I never babied him. Every dog will be different of course but I always find it easy to baby these little pups when they are terriers after all! Let them explore (safely) and learn about the world.
Here he was at 5 months old running in the snow.
https://www.youtube.com/watch?v=SDrJrq0ydRM
Use many treats, toys and encouragement! Consistency is key with potty training.
Pad training can be great but I find almost all dogs I know that are pad trained always make mistakes in the house whether it's on rugs, or just outside the pad, etc. It can be fantastic but I think it's confusing for many pups especially young ones. If I did pad training I would probably make it in a confined location or gated area with fake grass to simulate outdoor or having to go outside or w/e to go potty.