Yes, you read that correctly. Out of the four existing Winter Veil companions, only the Winter Reindeer persists when summoned outside of the holiday event.
The Tiny Snowman will only last a few seconds before falling over and "dying". I have to admit, it was quite a shocking and upsetting thing to see! Totally did not expect that. :( My poor snowman, I guess without that snowball to fuel it, it just can't withstand the heat of non-Winter Veil days.
Much like the snowman, the Winter's Little Helper and Father's Winter Helper don't seem to want to stick around either. They will briefly appear before doing a small conversing and "no" emote, and then promptly hearth (back to Father Winter's side, no doubt).
I've uploaded two videos showcasing two of the four Winter Veil pets. Winter's Little Helper and the Tiny Snowman. The snowman video is a bit heartbreaking, at least for me. T_T But who knows? Maybe some will find it hysterical, you snowman-haters! :P