I have no problems in grafting stone fruit (plums, apricots, peaches, almonds, nectarines etc) during the winter. As long as you remember 2 things.
1 – Stone fruit do not produce lots of callus tissue, unlike apples and pears. Therefore your grafting technique and cambium contact needs to spot on. Unlike apples which produce lots of cambium tissue, and will fill bad grafting techniques, ie joints where the cambium does not contact each other, or where you can see daylight between the graft union.
2 – Linked to the above, callusing temperatures for apples and pears have a wider temperature band. Whereas stone fruits need a temperature of nominally 16 deg C and with a relatively narrow temperature band. Apples can callus at 5 deg C, but stone fruits will fail.
In doing trials for home grafters, I also found the best place in the house that could maintain a relatively high temperature constantly day or night, was on top of the kitchen fridge freezer. This was nominally 20 deg C. So if you did not mind the tree growing earlier and a good callused joint, the top of the fridge freezer is a good start.
If you have no experience of grafting, then have a few trials on soft wooded trees, like willow or rose, just to get the technique right.
Cleanliness of pruners and grafting knives and treat/seal cut branches, as this could introduce silver leaf disease. We have no silver leaf round here, so I suppose we are fortunate. Also make sure you scions wood and rootstock is disease free.