For coloring the beard, Ben Nye's Snow White Hair Color will work nicely as a temporary dye. Just dip a toothbrush in the bottle and apply, then shampoo the color away at the end of the day.
For sweat resistant color on your neck and lower face...alcohol-activated body paints hold up the best against moisture, but they are pricier. As an alternative, you might test out a white creme makeup with a neutral setting powder and makeup sealer. Again, Ben Nye, a theatrical makeup line, is good for all of that.