I don't have personal experience with this, however, my host parents spent July in Iceland and had trouble going snowmobiling due to the fact that there was not enough snow to do it safely. So, though I cannot recommend an outfitter, I do think that you should research how the possibilities are. Try to contact an icelandic tour operator (Icelandair is very knowledgeable) and see what they say.

sorry, i did it a long time ago on a day trip from reykjavik and i can't remember the outfitter. it was a blast. unfortunately, i overturned the sled. nobody was hurt though.

I don't know if this is too late, but here goes: we had a great time snowmobiling on the Mýrdalsjökull - a glacier located along the south coast, not far from Vik. We went with Arcanum (http://snow.is/snow%2DEng/), which has a little lodge up on the edge of the Mýrdalsjökull. If you drive yourself, the road is pretty rough - I would be hesitant to go in a low-clearance car. The trip was great! It felt like we were out in the middle of nowhere, with a view of the ocean.

Here are some photos that I took:
http://mysite.verizon.net/res1dm2h/Pages/41.html

Taitai,
I wish I could give the right info you want but as someone warned, there may not be enough snow.

I caught on to your "passionate Iceland lovers group". The word Iceland captures my attention every time: it was my dream to go there and I did in 2003. I drove solo out of my Keflavik base and got as far east as the Jokull river.

If you're going to do something like that, please consider the small fee for travel insurance that includes medical evacuation. You might want to research what your medical insurance might cover way up there on the glaciers.

Have a baaaaaallllll!

TaiTai
It depends how how much snowmobiling you expect to do. If you are a hardcore rider and want to spend a few days on a guided ride, use one of the reputable outfitters there. We ran into the various adventure guides there and they all looked pretty good; new vehicles, well marked, etc.
If all you need is a taste so you can say 'I did it', then the operation at the Vatnajokull glacier is the most accessable. Just show up at the bottom of the hill in the morning, take the free van ride up, and go out with a group and a guide. You'll be done by midafternoon. Expect a 'liesurely' pace.
Weather will be a big factor. If it is rainy (most of the time) visibility at the top of the glacier will be 0.
In any event, bring money. Not cheap.