Just wear it !
Well ok, let's talk about the ins and outs of wig wearing in wet weather ;-)
First off it matters what type of wig you are wearing. Human hair and synthetic wigs react differently to water.
Wet weather is where synthetic pieces show off! Synthetic wigs hold their style and they don't absorb water the way a human hair does. With a little shake and a fluff you are literally back in business. Do you look like a wet rat in the rain ... yes but they dry faster and don't require a full restyle after a downpour. It looks realistic still and it does not become a tangled wet mess. A pat dry with a towel and a little shake can be all you need with a good synthetic wig. If you are home and able to take it off it's always advisable to put her on a wig stand to dry. BUT in real life when you have to continue with your day it's possible to just keep going and still have pretty terrific hair!
Human hair wigs are the same as our biological hair ! Yes you can wear them in the rain and they can get wet. The down side is that most likely you will need to restyle her after the rain. Unless of course you just give into the wet, scrunch it to coax the curls and wear her beach wavy. A pat with a towel to absorb excess moisture and even a quick blow out using the hand dryer in the ladies room is always an option to keep you going! I often will pull my wet wig into a ponytail or braid to keep her under control as she is drying. Just like your own bio hair, wet = humidity. Depending on the ethnicity of the hair in your wig, it can go curly or frizzy when exposed to humidity. The secret to keeping that frizz at a minimum is all about control! Sometimes the only way to recover on the go, is to put her up in a ponytail or bun or braid. Of course if you are going straight home you can put your products on her and give her a proper blow out and styling. Either way you can still have pretty natural looking hair after getting wet in the rain ;-)