The snow spider is a monster detailed on pages 154 and 155 of Frostburn (AKA It's Cold Outside) and has a poison listed as 1dx dex damage (based on spider size) and it has paralysis as a secondary damage, but it lists no duration. Errata also doesn't explain it, as far as I can tell.
A Dungeon magazine adventure that uses snow spiders provides a duration even though Frostburn doesn't
In the adventure "Raiders of the Black Ice" (Dungeon #115 17–35) by Wolfgang Baur—one of Frostburn's co-authors—, Medium snow spiders like those found in Frostburn (154–5) make an appearance. In that adventure, a snow spider's poison's secondary damage is listed as paralysis with a duration of 2d4 minutes.
Because a snow spider's poison's initial damage scales with its size, a DM may rule that its paralysis duration also scales—a Small snow spider's paralysis lasting 1d6 min. and a Large one's lasting 2d6 min.—as per Effect of Weapon Size (Dungeon Master's Guide 28).
Note: A similar information gap is present in Frostburn with the can-be-bought-for-gp poison snow spider blood (16) that has as its initial damage paralysis. The Dungeon Master's Guide on Poison (296) says that if a poison's initial damage is paralysis, that paralysis lasts 2d6 min. (Although that figure covers a poison listed in the accompanying table, the information is nonetheless presented in a general way.)