I believe there appears to be conflicting advice concerning "stratification" (eg place in a refrigerator or not) and if to plant the "pits" or the "seeds" (within), mainly because it really depends on the exact method of seed germination you choose to pursue...
GROWING NEW FRUIT TREE PLANTS FROM SEED (direct link to PDF) via Penn State University Department of Horticulture
The seeds of all common tree fruits (apple, pear, peach, and cherry) require a chilling
period before they will germinate and form new plants. The chilling period occurs after the fruit portion is ripe. This period is known as either dormancy or afterripening. During this period the embryo develops until it is mature. This is accomplished by subjecting the seeds to a cold treatment.
There are two systems whereby the necessary after ripening could be accomplished:
Plant the pits (or seeds) directly outdoors after the first frost of the year (normally sometime in the Autumn/Fall). The cold Wintertime temperatures put the seeds though their "stratification" period.
When planting outside in areas that go through freeze, thaw cycles you can get away with planting the pits, as mother nature will take care of breaking them open via seasonal changes.
Before planting the seeds (or pits) indoors, the seeds need to be put through their "stratification" period, this is where placing them in a refrigerator comes in.
To help increase the germination rate of indoor planting it's advisable to remove the seeds from the pits, when and how you do this is really up to you, personally I think it makes more sense to extract them from the pits just prior to planting ie After they've gone through their "stratification" period.
Extract seeds and/or pits from the fruit of which you wish to reproduce new plants. Remove all adhering fruit portions and allow seeds to air dry. Then, place them in a glass jar or other suitable container to which a loosely fitted lid or cover may be added. Set the seeds aside in a cool place until mid-January.
... in mid-January mix the seeds with either moist (not wet) peat moss, sand or shredded paper towels. Return mixture to the container and replace lid. Place container and seeds in the refrigerator until after the last severe spring frosts. The seeds should remain in the refrigerator for at least 60 days.
Of course you can accomplish the required "stratification" period via either "outdoor" or "indoor" (refrigeration) methods, then transplant the saplings or seeds to where you want them (outside or inside).
Good luck! I hope the above is somewhat helpful, makes sense and does not make things even more confusing - if I've muddied the waters further please let me know so I can try to clear things up.
Also let me know if you're interested in further reading material, I can post some links to articles, resources that I believe are helpful/useful.