1:58 p.m. on December 6, 2012 (EST)
Navigating in a whiteout or fog, or even dense vegetation, requires a set of skills that isn't talked about much, even in some of the best books on navigation. A couple nights ago, one of our local PBS stations had a program on the Donner Party. During the period they were snowed in at Donner Lake near present-day Truckee, CA, they sent several parties to try to get to Sutter's Fort for rescue. One group, called "The Forlorn Hope", ended up going in a circle for a couple days before they realized that they were following their own tracks - and that was dense woods combined with a blizzard.
I have spent a fair amount of time traveling through whiteouts and fog, as well as dense forest and jungle. It is a challenge, but doable with the right skills and certain pieces of gear. If you aren't prepared in advance, you may have to just hunker down and wait until someone comes searching or until the fog/blizzard/obscuring material clears up. Obviously, since I am still here and wandering the woods and hills, it is possible to travel through such conditions. However, GIANT CAVEAT - do not try driving through dense fog on freeways at speed. We get giant pileups on I-5, for example, every year that have involved upwards of 40 or 50 cars and trucks.
(1) Using a GPSR to mark the position of your tent before you set out helps. But remember that if you only mark the tent's position, the GPSR will you what direction the tent is from where you are, but does not warn you of cliffs, valleys, and streams between you and the campsite. You need to make periodic marks to retrace a safe path (continuous tracking will use up the batteries, so turning the GPSR and taking a mark every 15-20 minutes will save battery power and let you carry it inside your jacket to keep the batteries warm). Also, the GPSR accuracy is about 20 ft radius, but can be larger if you are getting multipath reflections from canyon walls or do not have a good lock on at least 4 satellites (too many "dumbed down" current GPSR models eliminate the satellite page, leaving you in the dark about the satellites - and, NO, the so-called "position accuracy" does not necessarily indicate the current accuracy).
(2) You can plan ahead and take compass headings from time to time (write them down in a waterproof notebook). You can retrace your path with these. Best way to follow compass headings accurately in a whiteout is to have a companion walk ahead of you and keep prompting them to stay on the correct bearing - a light cord tied between you helps keep things aligned
(3) Leave physical markers on your outbound journey. In snow areas (on glaciers, for example), you can place "wands" (basically those cheap bamboo garden stakes with a reflective or brightly colored ribbon wrapped around the top), or in dense vegetation, tie bright ribbons around head-height branches (remove them and collect the wands on your return journey). Climbers on glaciers are generally roped with about a 30-50 ft interval, so when using wands that you place every rope length, you can stand at one wand and have your buddy go out a rope length. S/he should then find the next wand. If not, you know the distance, so your buddy can sweep side to side until you find the wand.

In this photo, we were using a combination of techniques - we were following a wanded path, roped, and the path had been somewhat packed, though snow was drifting into the path, making it less visible. We had to go about 2 miles through this stuff, finally coming into the clear within sight of the campsite.
I suppose you could use a beeper or a radio homing beacon (the ham radio "foxhunt" type of searching). But that depends on the transmitter's battery lasting long enough.