Snow button will prevent it going into 1st gear, ie take off in 2nd and I think change gears lower in the rev range.
Also, not a good idea to use the synchro button on hard surfaces at speed, only on grass, snow etc when you need it. Puts stress on the transfer case, especially when cornering on ashphalt. Ive only ever used it when on wet grass or at the boat ramp etc.
PS welcome by the way.
You won't need an owners manual, theres more info to be found on this forum, just about everything has been covered a few times over.
Ive got the full Japanese workshop manual, can be handy if you can work things out from the pictures, and also if you want to know a little more about your car, pm me your vin and ill send you what options your car came with.