as already stated, sand is about flotation, not traction, a highway terrain tyre in passenger construction is the best tyre to have, the sidewalls are piss weak and bag out super well, there are no real big gaps in the tred to fill with sand and act as shovels.
whereas aggressive tyres tend to act more like shovels that said, there are a few disigns which work very well on sand. the tractor tyre look like procomp x terrains and baja claws are great on sand, they have large tred blocks that still sit ontop of the sand and the oversize tred blocks dont dig in as much. the angle of the tred also helps alot too.
most A/T tyres are a pretty good happy medium that will do more than fine on sand and still cope with most 4wding except the really sticky mud.
most at tyres have a similar construction as mts, the only real difference is the tread pattern. the way that the belts run, the radial plies, sidewall construction and stiffness etc are very similar if your comparing apples with apples. i say this because many at tyres come in both passenger construction and light truck construction (LT) wheres as most muddies only come in a lt construction. (see your side walls they will say "LT" in the tyre size ( ex LT305x75r16) if you plan on using your at tyres on more than justyour average gravel road or if your loaded near your gvm then you should definitely be running the LT construction, but if you are like many of those running your zook soley as a fishing bus and it never gets loaded up with heavy gear, then a passenger AT type tyre would be a good choice.
passenger tyre sidewalls arent as stiff as LT type, therefor you can run higher pressures to get the same bagging effect offroad, but you risk sidewall damage in anything but sand.. example, a 285x70r16 passenger tyre would do quite well on a near empty patrol wagon on the beach running 22 psi whereas the same vehicle in a lt type constuction of the same tyre would need to start at around 18psi to get the same effect. then those with more aggressive tred patterns would again need to run lower pressures to get a more floating effect in the soft stuff (say starting around 15 psi)
the lower you run your tyres the more risk of breaking a bead on the tyre when cornering.
what ya need to do befor buying tyres is to work out how much of each type of terrain you plan on driving in and make a more eductaed decision as to what type tyre to get.
personally i run mickey thompson MTZs, these tyres are classed as an LT mud terrain, but in reality they are more like a very aggressive AT tyre. the LT construction means that my fully loaded GQ patrol is easily carried and i have a stronger sidewall construction.
the benefits i get is that i can have the confidenece that when on the rocks or in the sticks, i have a better chance of safe passage without a flat, i can carry more wieght with the tyres staying more upright protecting my sidewalls more. also the design of these tyres have sidebiters, which again help with sidewall protction by deflecting damaging sticks and rocks slightly. the cross ply technology in these tyres is great too as the handling and stability of the tyres is greatly increased too........
when looking for tyres, its not just the tread pattern you need to consider, its not just the sidewall plies either, it is the tyre as a whole unit that you need to look at. certain tyres suit different drivers, different vehicles, different terrains, different wieghts etc all differently and the bloke at your tyre shop very rarely goes into this, because its all about making the customer happy right then, not 3 months down the track, they tell you what they think you want to hear then make a simple sale rather than having you go down the road and get the tyre that is best suited to you..
things are not all equal with tyres and different brands are not all the same, (even those built in the same factory) fully examine every aspect of the tyre befor you choose, ask questions, and most importantly be patient, dont rush into a purchase because they look good, or because someone else has them on thier rig