Originally Posted by Bignose

In theory, the momentum in perpendicular directions will be independent. That is, if you are hitting a ball straight downrange and there is a crosswind at exactly the perpendicular left to right or right to left, the drag from the perpendicular direction will only move the ball left or right, and should not change the momentum in any other direction. It does depend on what you mean by "total distance" because the distance downrange will be exactly the same, but because the ball moved side to side, there will be more "straight line" distance between where the ball started and stopped.

It is the difference between moving along the side of a triangle or the hypotenuse.

B________C
|............../
|............/
|........../
|......../
|....../
|..../
|../
|/
A

The downrange distance is from A to B, and that shouldn't change no matter how much crosswind there is. But, with a left-to-right cross wind, the ball will travel from A to C. And A to C is equal to or greater than A to B, based on a simple mathematic property. It should be noted that if the wind is constant, the ball will not travel on a straight diagonal line, it will curve very similarly to a drawn or faded shot.

All that said, the point above about how rare pure cross winds exist is pertinent. It would be exceptionally rare circumstances that there isn't some upwind or downwind component to a shot, as well as some vertical component to the wind. So, it's always going to require practice/experience. On the calculation side of things, it is important to know that drag is in the neighborhood of a velocity squared order of magnitude. That means, that the drag increases as the velocity difference between the ball and the wind squared. It's not exactly a squared phenomena because of the nonlinear nature of the turbulent fluid mechanics, but, it is not linear in the typical range of golf ball speeds. In short, hitting into a wind costs you much more than you can get from hitting with a wind. If I remember correctly, a drive that normally carried 250 yards loses 14 yards into a 10 mph wind, but only gains 6 yards with a 10 mph tailwind.