My experience is that it depends a lot on variety. If it is roses that easily produce suckers like Great Western, some gallicas, rugosas (and many others), or is known to grow well ownroot in your area, it can safely be done. You might have to prune them rather a lot for the roots to be in proportion to the rest of the plant.

If you have varieties that benefit from the vigor of the rootstock, it will be a different story. Most if not all hybrid teas, floribundas and the varieties that looses most of the canes above ground after winter will probably do better keeping the rootstock.

I agree with taoseeker on the variability.
I'm a bit warmer than Donna, and I've moved a lot of our roses. Roses do what roses want to do. Some will put out roots within two or three years from the part of the scion that's buried and above the bud union.
I have also seen a very old rose moved that still had the bud union, but the scion had grown out into about eight separate-able bushes, and the bud union was almost rotted out. The big bush fell into many bushes the first time it was rested on the ground. (This particular floribunda probably does better grafted, on its own roots, the canes aren't as vigorous.)

When you move them, you'll see from the below ground parts if the rose is trying to go own root or if it's happy on rootstock. (Sniff to see if the original rootstock is fresh or if it's rotting and dead.)

Follow the lead of each rose.

I just dug up some old roses last fall. I just planted them. You'll need to dig a BIG hole to spread the roots out. The only thing you need to trim is broken roots. Go ahead and plant it as deep as it was. You now have a very hardy rose that won't require winter protection, cause it's on it's own roots. Leave the bud union alone. The bud union is the big fat knobby thing, if you don't know what it looks like. Make sure to add some organic matter as you plant it. Then cover the canes with mulch as much as you can so the canes won't dry out. Then water it in!

Donna,
I've done this for years. My experience is the buried canes above the bud union will grow a big network of roots. When this happens the old rootstock ceases to be a factor in the plant's growth. When dug up the old root stock is bare of fine hair like roots and, for the most part are just anchor roots. When I moved eight years ago, I dug up all my 550 roses, potted them, and brought them with me. In most cases I was able to get three or more bushes from each bush. I cut the canes off where they connected to the old bud union. This gave me a well rooted own root bush. My Touch of Class was separated into seven bushes and I still have one that's turned into a very nice plant. Although the hybrid teas die back almost the the soil line each winter, new growth come up from the roots and by late May, have developed into large healthy bushes. In all cases I remove the bud union and it's root stock. Bushes that don't grow well on their own roots will not have grown many roots of their own. In that case you leave the bud union and root stock attached.
By looking closely at Mom Nature's work you can determine what steps to take with any one variety bush.
An own root bush may develop a pseudo bud union at the soil surface after awhile from where the canes seem to grow. if you know for certain a bush is own root and you find what appears to be a bud union, rest assured it's still an own root bush.

Thank you all so much..that answered all of my questions ! I will play it by ear as I go...my roses aren;t even leafed out here yet, so I will do okay transplanting them. Donna