A few minutes won’t hurt him at all. Just make sure he is properly contained, and that he is dried off afterwards. Bunnies can take cold, but dampness can hamper their immune system and make them sick.
I took one of mine in the snow recently and my little brother threw a snowball at him. So be sure to protect him from children too lol.

I took my Vilde out in the snow when we had snow here a couple of days before Christmas. He was a little surprised about it, but he hopped around and dug a little hole etc.

I dried him well when we came back in. He seemed to like sitting in my lap to get dried, probably because his paws were a little cold. Because he’s a very fluffy bun, some lumps of snow had stuck to his fur so I had to pick those out.

ETA: Here’s a pic of Vilde in the snow:

Vilde was harness-trained long before I got him, so he’s totally unafraid of getting the harness on. If your bun isn’t harness-trained, I’d not recommend you put a harness on him for his first time out in the snow. It’s much safer to try and make a simple enclosure. 

Some people bring snow inside for their buns. Either in a big container or some snow in the bathtub. I tried this when I had my Bindi….he was not impressed by the cold.