Thank you all who replied up to now.
I usually snuggle my cat's fur - he won't scratch me - because he's got the most amazing fur ever! And I like to bury my face into my pillow, my hands or a book (which is, no doubt, a little hard and itchy) too.
Admittedly, I've also done it with other people's pets before, when I could not remember that it might be odd. I know not to do it with other people, I did it when I was younger and learned that it was very very inappropriate early. My family is the epitome of good manners and social rules, it's insane.
But I haven't yet thought about that it might disturb another person if I snuggle their pet in a too intimate way! I feel kind of stupid now, boy, this is embarrassing. I do feel bad if someone touches my pets too much. So it makes perfect sense others may just see it the same way as I do.
I'm glad I'm not the only one who does this too. I received some very dirty looks about it as if I had missed out something. I was already wondering whether it might be disgusting or not hygienic. Got worried there for a minute...
I've always done things like these though too!
When I was little, I usually did the 'Eskimo kiss'. That's what my grandma called it anyway. We usually rubbed our noses against each other instead of welcoming and good-bye hugs, kisses and other kinds of more typical affectionate gestures.