I have taken rose seeds from my garden and put them in the fridge between moist paper towels.
Does anybody know what size pot I should put the rose seeds in that have germinated in the fridge?
All plants should have pots matching the plant size, otherwise you risk root-bound plants or trouble with watering. That's why we re-pot as needed and only go up a few pot sizes at a time.
Roses like to go deep with their roots, so I would aim for a pot of ca. 5 cm / 2 inches height right now, once the seedling is established, take it from there.
Generally, roses prefer pots that are deeper than wide or, if those aren't available or feasible, let the height be the determining factor rather than width. If you want to keep them in pots permanently (And not all roses like that - especially with seeds from grafted plants you may be in for a few surprises!), they tolerate an undergrowth of shallow-rooted companion plants well to utilize the "extra width" in standard containers.