One suggestion is to buy dried mushrooms and rehydrate them when you need them.
As for freezing, as you probably know if you freeze them and thaw directly without any intervention you will probably get brown, mushy mushrooms. There are a few ways to avoid this.
If you blanch the mushrooms first in some boiling water, then put them in an ice bath, that should stop the enzymes that cause the browning and also help with the texture some. This method should also retain the most flavor of any of the preservation methods.
As a side note, I highly recommend going from freezer to cooking directly without thawing - this should reduce the amount of mushiness you will get.
I find that slicing and sauteing the mushrooms first in some oil or butter, then freezing them, works great for most uses, since sauteed is how I usually prefer my mushrooms anyway. I just take them out of the freezer and throw them directly into the meal.
In my house the most common method is as I first mentioned, we buy dried portabellos etc and just rehydrate them into our meals. However blanching and then freezing is often better for texture and taste, it just takes a little more time.
There are some great mushroom preservation methods available on this site.
I suggest you read the transcript to the Good Eats show on freezing, or, better yet, find a copy of the episode to watch. (Good Eats is an American TV show focusing on food science.) Here are some relevant excerpts:
[In the freezer,] any present bacteria are going to have a devil of a time finding the moisture they require to live, breed, survive. Since they themselves contain a considerable dose of H2O, freezing halts bacterial activity altogether, though some of the little beasties can survive to decompose another day. While it is in this frozen state, the meat will remain unspoiled for years. But there's a problem. You see, home freezers work very slowly. That means that as those little H2Os start to line up inside, they'll create huge, sharp, jagged crystals that will rise up, slicing and dicing their way through cell walls, muscle fibers, and pretty much anything else that gets in the way. Now while frozen, you won't notice this damage. But when it comes time to thaw, all of those perforated cells will start to leak out moisture all over the place. It's called drip loss and it's not a sign of good eats.
Therefore, if you are buying the meat fresh (i.e., it is not already frozen), then you need to take special care in how you freeze it:
One good way to prevent drip loss is to freeze the target food very, very quickly to a very, very low temperature. So that instead of creating huge, jagged, nasty ice crystals, you get very, very tiny little ice crystals.
The episode goes on to describe a process for freezing meats at home (basically, the idea is to use small pieces of meat, freeze them separately on a sheet tray, and then once they are frozen transfer them to a bag for long-term storage).
Even though the meat will technically be safe to eat for years, there are a few caveats. For one thing, the environment in the freezer is very dry. That can cause moisture on the surface of the meats to sublimate and form ice crystals, otherwise known as freezer burn. This can be avoided by packaging the meat in a vacuum (e.g., vacuum sealed bags), however, if you don't have a good vacuum sealer, I would suggest limiting their freezing to 6 or 8 months in order to avoid freezer burn. Another reason to make sure you use an air-tight container is that fats are very good at picking up flavors of other items you might have in the freezer.
I am fairly certain the "fats will surely go bad" claim is a myth, especially since fat alone is a good preservative. Perhaps you should ask that question on Skeptics.SE.
Best Answer
Frittata freezes just fine. At least, mine do. There are a couple of drawbacks you might want to take into account when making your recipe, though.
One is that the individual tastes of the ingredients all meld together when the frittata gets thawed or reheated, so if you're looking forward to that bite that has a particularly strong taste of, say, asparagus, it's not going to happen. Conversely, if you're looking forward to that bite that doesn't include the taste of green pepper, that's not going to happen, either, if you put it in there. I never use green pepper in frittata; it completely takes over the dish.
The other drawback is that some of the moister ingredients will lose water upon thawing or reheating, thus soaking the frittata on the second go-around and giving it an unpleasant, rubbery texture. If you plan to freeze your frittata, consider your ingredients with that in mind, and choose ones that are low-moisture (extra cheese, dried ham, etc.) or pre-cooked to cook out some of the moisture (mushrooms, sweet onion, etc.)