One nose I like is Dumbo's....you know, the baby elephant? I like elephant sneezes, as well, and his is just the cutest thing ever. I love the scene where the Elephant Matriarch gently tickles his tiny trunk, he crosses his eyes as his tickly lil trunk starts to wiggle and twitch, and then it curls up tighter and tighter as he builds up and gets sneezier and sneezier.
And....I know this particular character isn't "furry," per se, but I've always loved Susie the little blue coupe's nose.

It's just so cute, isn't it? It's all snubby and pointed at the very tip, and I've always imagined it would be fun to tickle it with a nice, soft feather, or just by ever-so-gently running one or two fingers over and around it in playful, tickly gestures. I'm almost positive Susie has quite the sensitive, ticklish nose, and enjoys nose tickles a lot.
