The easiest rose wood to root is called semi-hardwood. It's the age of a stem that has recently produced a flower. So the cuttings are a result of deadheading, not spring pruning.

Hardwood cuttings are a totally different method. The idea is to take old wood, stick it in the ground, and leave it there. Very easy, but not as reliable. I've done those in the fall, and done very well with some varieties, terrible with others. To even think about doing that, though, you have to start with varieties that are cane hardy.

If I even find out I have room for a hedge of Jacques Cartier, hardwood cuttings are where it would come from.

I use the method in the article for rooting roses outside. Last summer I started 24 roses, repotted them all after they had rooted well, lost one for unknown reasons and another by being dug up by squirrels or chipmunks (I made a chipmunk swimming pool and got rid of 9!). Last fall, I planted 22. The results are consistent year to year.

Here is a link that might be useful: Rooting and Overwintering

thank you I"ll try that method next. During which months do you try to start to root? I know their little roots have to be somewhat developed before it gets cold so there has to be a cutoff point in there somewhere. July-August depending on the variety?

Also, do you have any recommendations for easy to root shrub varieties? I do have room and want a rose hedge perferably 3-6' tall, red/apricot/orange or yellow rebloomer with a strong fragrance.

Off hand, Knockout is an alarming red that grows to about 3' here in the Great Lakes, but is still under patent. Eutin is an old Kordes rose which should root easily, but has no scent. It grows to about 5' here.
Steve.

I forgot to answer when I take cuttings: usually after the first bloom in late June or early July, though I have taken cuttings as late as the middle of August, but those may not get large enough to repot before winter sets in. Friends of mine may plant the pots to overwinter them if they don't have cold storage somewhere and are not convinced the newly rooted cuttings are ready to fend for themselves in the garden.
Steve.

The standard for a hedge in a cold climate is some sort of rugosa. They aren't the easiest roses to root, but do spread by suckering. Those can be dug out and moved at pretty much any time.
Without a better idea of where you are, I really can't say much more. My zone 5 is, for a variety of reasons, much harder on roses than zone 5's further west.

Nebraska - close to the Missouri River (I think it's a mile and a half to the east from my house)

Mad Gallica, of course, is right. If you are looking for a true hedge, which only needs a bit of spring pruning and, every five years or so, the oldest canes removed, then rugosas are the way to go. The ones I mention will need to be pruned to near the ground, but will come back each summer to height.
Steve.

Easiest way would be layering. Not the fastest way by any means, but easy and highest success rate.