Mountain bikers have enormous fun chasing down mudtrails, crossing rivers and jumping off special ramps into lakes. Cycling in the rain is great fun with the right gear.
If you're into mud and spray, take the mudflaps off and speed down some muddy field track. Try it some time. You might enjoy it.
Remember that chains and bearings do not like water. Unless your bike has sealed bearings, like good mountain bikes have, it is perhaps better to find other ways of suddenly ending up in the water with a big splash.
In any case, careful cleaning and lubrication of your chain is required afterwards! It is also quite easy to hurt yourself, unless you know what you are riding into.
T-shirt or cycling shirt, cycling tights, anorak with rain pants, socks and shoes with a good grip are a good start. When these clothes get wet, they still protect you from windchill and sunburn. The key is to pick clothes that dry quickly and feel good even when wet.
This is a seriously muddy game, not just for the riders. Even the spectators get muddy as they watch from very muddy fields next to the tracks and get sprayed by passing riders. Get in the first four rows of people and you usually get covered in mud from the spray.
If a bike gets stuck, they try to get it out usually by giving it full throttle and the crowd usually ends up in mud/water everywhere. Dress accordingly.
Some tracks have a pond in it and the track goes right through it. The spectators standing right on the edges of the pond get soaked every time a rider comes through. Great fun.
If you're going to on any beaches/streams/sea, or any public footpaths, tracks or parks the you require a motorbike or moped driving licence.
Depending on the size of engine up to 50cc moped licence is fine. Above that you need a motorbike licence. You also need insurance and a road legal bike (i.e. O.K. tyres, tax, mot, etc).
If you go on proper tracks or if your mates got a large field or somewhere you can do it then you just need the bike and maybe safety gear.
You'll need a crash helmet unless you're doing it on private land, then it's up to you it you use one or not. Some tracks require you to wear the proper protective clothing, others don't.
If you're going faster that about 40kph you need some form of eye protection.
It really hurts when the wind hits them between 60-100 kph.
Usually MX riders don't go that fast.
The ones that do either have helmets that'll keep the wind off their eyes, or wear some form of safety goggles.