Not a real worry.
The wood is going to have to live in that environment with the stove anyway. It's going to dry to the average moisture content of the room eventually, and then vary with the seasons. If your wood is ~15% you can (and should) bring it inside and let it finish drying. If you measure some wood thats been inside for a long time, then thats the MC you want to aim for. It could be anywhere between 6% and 14%, depending on where you live. 8% seems a good average for inland US areas.
Bringing green wood inside with the fireplace can cause problems with drying too fast and splitting / checking etc. But at 15% it's done 9/10s of the drying and is pretty difficult to stuff up now
Cheers
Ian