No trimming your nose hair doesn't make it grow any faster although it seems that way.
Trimming the nose hair just gets rid of the nose hair and then it will just grow back and you will have to trim the nose hair again to keep it out of your nose.
Your nose hair will always grow back and when it's been trimmed it seems like the nose hair has grown back at a faster rate than it normally would if you didn't trim it.
But in reality the nose hairs are just growing at the same rate as they always did and trimming the nose hairs as often as you want will not make the nose hairs grow any faster.
My husband trims his nose hairs and it does seem like they grow back faster but they really don't.
He trims his nose hair every few weeks as they start to grow back because he hates having nose hair because his boogers etc gets tuck in the nose hair which he finds to be gross.