Why can’t I make blueprints

What I did was ensure I had a really large stockpile of catnip. I saw Winter was coming, and so I stopped spending catnip. That allowed me to have enough catnip to survive, even without farming.

But as you noted, you now have farmers. Once you get past four kittens, just living off of the stockpile of 5,000 isn't really enough. Most kittens should become farmers during winter, so that the rest of your population doesn't die off.

Another option is to build a barn or two, and make your stockpile even larger. The more barns you have, the more kittens you can support through a winter without farmers. Some later technologies allow you to build things that allow your kittens to require less catnip, and you can stretch it just a little bit further.

Generally, though, farmers are your best go-to for ensuring your population survives.

Faith, on its own, can't be used for anything at all without converting at least some of it into total faith on the religion screen. As you Praise the Sun, you'll unlock various upgrades on the Religion screen, many of which get stronger the more faith you convert.