Going through the equipment lists, I see no special reason why anyone would bother to buy a bedroll or a tent, since they do nothing. However, a blanket is part of the basic loadout, and tents are offered as an upgrade, so they should do something. So, this is me thinking out loud about how to handle them.
The other lines on this table bring up good issues. Plate armor knocks off four hours, which sounds about right; call all rigid armor knocking off half its DR in hours, rounded down. No loss for flexible armor; I think it's now a moot point that you can sleep in mail without much problem. Being below 0°F (or 35°F lower than your character's own low temperature threshold, for anyone with Temperature Tolerance) takes off another hour, while being above 90°F (or whatever your Temperature Tolerance gives you) takes off two hours.
Now, if you're hex crawling, missing sleep would have its normal effects, which means you're down FP. If you want to sleep a little longer, that will cut your travel time, so each extra hour cuts off 10% of travel, since I assume 10-12 hours of actual travel to make Move = 5-to-6-mile hexes. If you're using the slewing way of travel (hey, remember slewing in Microsoft Flight Simulator?) in GURPS Dungeon Fantasy 2: Dungeons, rule that not having a blanket means you get to wherever 10% slower, while not having a sleeping fur in winter or arctic weather means you get there 20% slower, or 10% slower with a normal blanket.
Some other lines in this table from the Wilderness Survival Guide lead us to tents. If the wind speed is 20 m.p.h. or greater and you have no tent, it says to dock two hours. If there is light or moderate precipitation and you have no tent, it says to dock three hours. (Those in plate armor don't take this loss, so if the weather is bad and you know it will be, it might be better to sleep in your plate.) And, in the graf below the table, it says that you can't sleep outside a tent in "extreme weather conditions," listing a lightning storm, a hailstorm and a sandstorm as examples. All of this I am going to use as-is for my hex crawl. For travel without detail, give a bonus of +1 to the Weather Sense roll to lower travel time if there are enough tents for everyone.
GURPS Dungeon Fantasy 1: Adventurers and the Basic Set both call this "[b]asic equipment for Cooking and Survival for a group," which sounds well and good until you realize that there's no special group Cooking or Survival rules anywhere. So, we'll handle this like the tent: having Group Basics means that you get a +1 to foraging rolls since the gear lets you better skin and prep the food to make it last longer and get more off the bone.
(Note to my players: wow, I hadn't looked at the Survival skill in ages. You all will hate those daily rolls.)
Throwing This Open
Anyone have any ideas?