If she's healthy, she'll do well without a blanket :) fluffy coat is no different from normal coat, really. It just takes more time to dry. She should have access to a "safe" area (safe from the wind, safe from the rain, safe from the mud) in case she wants to use it.
If she gets muddy (and then the mud dries) you brush, and brush, and brush... until you clean the parts of the horse where the saddle, bridle and girth go. Don't worry with the rest of the horse unless you like to have her clean. And spend two hours grooming. The horse doesn't really need to sparkle, but you need to check that under all that mud there are no cuts.
If the mud is wet, you should try to dry it with sand, or straw, or whatever, and then brush it off. Just don't saddle a muddy coat, because it can cause frictions and sores.
After riding, you should have a couple of fleece blankets to put on her and then walk her until she's dry. You usually end up having a wet blanket, and then you change it with another, and you remove the last when you're positive her skin is dry.
If it rains, you might consider covering her under a roof, and let her out without blankets when she's reasonably dry and you're sure she have a normal "at rest" breath/heart rate.
To be sure, check how she is before you ride, you should return her to the pasture no more wet/panting than that.
If the ground gets very muddy, you will want to put some fungicide under the hooves. I just know the common name for it in Italian, so I don't want to translate badly and advice something different and harmful, check with local horse-owners, they should know one and how often they use it.