My stock height D40 (supposedly not as capable as a D22, but the jury's out on that) with the original continentals didn't mind a shallow ford:
nor did it mind a modest river crossing:
and to top it off, we actually found some mud. I went through first, stopped IN the mud and took this photo, then climbed in and got going again. On standard tyres.
It's possible to do, you have to be careful about your diff height and don't let the wheels spin too much.
All Terrains are better, of course, but there's no need to throw money away. Depends on what you want to do. Best take a friend in their vehicle in case you DO need some assistance.