Correct, fresh tires make a big difference, as does lower air pressure.
Being on a 125 I guess I don't have to tell you to keep it pinned WFO...
Letting off the gas will cause the front end to knife in, even if you have your weight back. Stay on the gas at all times, then use slightly less gas to lose speed, but stay on the gas and on top of the sand.
The bike will move around underneath you, so just go with the flow and hang on loosely. If you get into whoops, keep your front wheel up and hit things mainly with the rear wheel. If you let your front end get low when landing in the sand then back off the throttle, you have a sure-fire way to dig the front end in and get tossed off the front or over the side.
Hope this helps, TexKDX.