The tattoo was clearly a bad example. Maybe this is a better one, is it really out of line for a wife to say "honey, I would really rather you didn't style your hair in a purple mohawk."
I guess its kind of a moot point but I really don't think a purple mohawk is line with simply cutting ones hair a bit shorter either. A purple mohawk will affect more then just appearance (employment prospects, ability to get into formal establishments with strict dress codes, etc) and costs money to reverse* and is an extreme style (presumably your example is in reference to someone who does not start out with an extreme/outrageous style).
Your wife cutting her hair is comparable to - you cutting your hair (for a man with short hair already the comparable would be shaving one's head, for example, which like shorter hair on women, is currently a quite popular look for men). Shorter hair on a woman is still widely social acceptable, still within general dress codes, and will grow back for free.
Its unfortunate you seem to feel so strongly negative towards your wife's current hair cut, but it will grow back in a few months.
*Yes eventually the shaved parts will grow in and the purple will grow out, but in order to look presentable say tomorrow or in a 1 week, etc it would cost money to re-dye the hair and come up with a style solution.