It's very possible that your new little kitten was carrying a bug that he has shared with all your other cats. If the stuff that's coming from their noses is clear, I would give it a couple of days, up to a week, to see if it clears up.
If the mucus changes color or your cats begin to act lethargic or seem visibly sick to you, a vet visit might be needed.
Did you have the new kitty tested for FIV/FelV?
If not, I would so so right away to rule out any communicable viruses that your older cats could catch. FIV and FelV are both highly contagious and both severely weaken the immune system.
So, for now, I would watch the mucus that's coming from the nose. If it changes color or the cats get worse, you will need to take them to the vet. Some of these bugs just run their course and are over with after about three weeks.
Some vets will allow you to bring in just one of the animals to examine. You can explain to them that all three have the same symptoms and ask if they can treat all three the same. That's up to each individual vet.
I hope this helps!