How much should one apply? Two or three inches is a good depth. Less than two and the beneficial effects dwindle rapidly. More than three and the plants start to treat it as a kind of topsoil - and mulch is not a very good topsoil. This is a bit less of a problem with deeply rooted roses than it is for other cultivars.
A west-coast rose grower advocates piling mulch over most of the exposed canes of a new bare-root transplant, then removing the mulch when the rose leafs out. This limits dessication, a major reason for failure in new transplants. To be successful with this strategy requires a little more than three inches of mulch to be available. In any case, following this instruction has proven successful.
People in northern climates will sometimes pile mulch six inches or even a foot high to protect frost-tender roses. This is usually preceded by pruning the rose to a height that roughly matches the depth of mulch.
In the spring - as the tulips blossom - the mulch is pulled away from the rose. This solution works. There are more high-tech insulation blankets available for this purpose.
The head of a prominent garden in Quebec pulls the stems of roses down to the ground instead of pruning them. Then she protects them with a polyfoam blanket. Where rose stems are pliable enough to do this, it can work well also.
Mulch improves the quality of life of a rose in several ways:
All sorts of materials are suitable for mulch. Some commonly used ones are pine needles, pine bark, wood chips, chopped roots, coconut hulls, cocoa hulls, and peanut hulls.
I can't think of why compost might not be used, or rotted leaves. Sometimes rocks and gravel are used as a mulch. This works to some extent, but it is less effective in most of the categories, and it does not help feed the soil.
Do not use grass clippings or unrotted leaves. They will decompose quickly and while doing so will eat up nitrogen and other nutrients. Material such as this that have been composted can be good, but they will disappear quickly into the soil.
The best mulch is a compounded mixture of grass or manure and woody materials. It has a carbon to nitrogen ratio of 14:1, a pH that is nearly neutral, around 7.4, and is rich in the kind of minerals that plants use: potassium, calcium, phosphorus, magnesium, iron, zinc, sulfur, and so on.