As Mark notes, most fields (or rather, their insurance companies) have specific rules on goggles, and restrictions against modifying them.
That said, people do still "modify" them, typically as part of a costume for a big scenario game or the like. But generally speaking, those mods are added to the goggles, not a structural change.
In other words, most fields wouldn't let you use a mask that you made yourself, even if it was attached to an otherwise unmodified pair of goggles, but they probably would let you use a mask that was itself unmodified, to which you'd attached your costume bits.
Make sense? I suppose we should clarify that "goggles" are the part that holds the lens and surrounds your eyes, while the "mask" is generally the part attached to the goggs, that surrounds and protects your face. Both words, however, are used more or less interchangeably to describe the entire helmet, when referring to it as a single accessory.
So your best bet, if you want such a thing, would be to mold the nose or muzzle or whatever, so that it attaches to an otherwise unmodified mask.
One technique to mold said nose is pretty involved, but should give pretty good results. First, either start with a "sacrifical" set of goggles (probably preferred, as there'll be some solvents that might degrade the lens) or carefully cover the good set with something like blue painter's masking tape, being careful to cover every seam, and to not leave any wrinkles or excess tape.
Then build your nose off of that. Sculpey, sculptor's clay, foam, that two-part plumber's epoxy putty, paper mache`, used bubble gum, whatever. Sculpt it into the shape you want, putting in all the details and textures, etc.
Once it's cured or hardened, coat it with release, and lay up a fiberglass, plaster or even silicone negative mold on it.
Wait 'til that cures, remove your plug, and use the mold to lay up a proper fiberglass positive copy. Let it cure, trim the edges and check it for fit against the mask, paint it appropriately, and attach it to the helmet with several zip-ties.
Working with fiberglass is messy, and you're looking at several days and a fair investment in materials to do it that way, but the end result will be- if you do it right, and I've left out a lot of details- a strong, durable, lightweight add-on that should fit... well, like it was made for it.
If you're really talented, you could make the add-on part look like it's supposed to be the mask that covers a canine nose, rather than the doggie nose itself. Might want to take the time to mold matching "ear" armor though, else all the other players might wonder if that weird mask is covering some gross deformity or something...