If all dangers of frost have gone (here in Scotland we've just had below freezing for several days but tonight it has gone back up again)
I would get a good pair of gardening gloves, nice sharp snipers or larger loppers depending on thick the wood / stems are that require pruning.
March / April is best time here for this job, Begin by cutting out any dead wood / stems, then move to any stems that have grown crossed over any other stems,
Then look for any stems to cut out that are diseased , browned by frost or split by severe winds.
ALWAYS cat at an angle 1/4 inch above an outward facing bud that by now should be very evident along most stems, also remove week / thin stems back to an outward bud, when cutting at an angle / slope, make to angle that slopes DOWN from the outward facing bud as this prevents rain or self watering moisture to land and settle on the bud causing it to rot.
I try always to cut back hard to about two thirds on strong stems and it also encourages larger blooms, and less hard IF you want more flowers over the season,
Clusters of flowering climbers (small bunches of flowers on each stem) Floribunda Roses, get more gentle pruning than larger flowering climbing Roses but IF your particular plant has gotten completely out of hand, a good hard pruning wont do any harm early on in the season (NOW) as this will give time for the rose to recover, put on lots of fresh new growth that you will be able to manage better next year come spring or late autumn if thats better, I prefer spring pruning as winter frost can kill lots of stem ends.
After this type of work had been done, I always weed around the base (root area, add a good Balanced Rose fertiliser / feed and gently hand fork it into soil trying not to break any top roots just under the soil.
This is also a good time to step back and took see what or where you need to retie the stems back onto the Rose arch / Frame, I use ladies OLD tights as they are soft, strong and stretch which allows the stems to grow / swell and as the stems get longer, just tie those onto frame, the foliage will hide the ties and wont be seen, they are easy to cut free also when needed. Best time to tie the stems are when they are softer and more pliable as when too hard / thick they don't bend to shape as easy.
Tons of great info from WeeNel!
I would like to add that all year round you can do some light pruning of roses.
For example, you want to cut some roses to display in the house? THAT is pruning- Make the cut in the best place for more growth to grow where you want it. Some roses will bloom over and over again when they are cut right. Other varieties just have one main crop of flowers. When that main crop is done you direct the pruning to cleaning up and helping the plant store energy for next year.
A stray branch is just going crazy? Prune it sooner rather than later. Again, pay attention to the buds you leave, almost always the top one that you leave is where it will continue growing. Sometimes several near the top will grow. If too many grow, or some in the wrong direction, rub them out when they are soft enough that your fingers can do the job. Barely expanding bud. THAT is pruning. Then the plant will put its energy into growing where you want it too.
Watch out for branches that are coming from very low on the plant, especially underground. Most roses are grown in 2 parts, grafted together. The lower part is a sturdy, disease resistant root, but does not have showy flowers. The upper part is the part with the beautiful flowers. If the branches are coming from below the graft they should be removed as soon as you see them. Usually the graft is pretty obvious, but not always.
It's best not to procrastinate when it comes to pruning climbing roses. It is very important to know when to prune these once- flowering climbing roses. It should only be done right after the flowering flush is over.These roses mostly bloom on old wood, so if you prune them in spring, you would have no flowers for that season.
I Nelson, I think it's important to prune our Rosed according to the seasons we have here in UK, Most of the UK will end up with bare stems from Autumn, then frost damage to the bare stems IF temp falls too low, the frost, Severe wind damage we also get here means it's Autumn or EARLY spring time for pruning most Roses.
Autumn is generally a light pruning as this helps prevent the bushes from being rocked and loosening of soil around the roots, or the longer branches rubbing against each other as this allows disease to enter the damaged wood / stems, it also helps prevent the longer stems breaking in the stronger winds..
Spring (Early) is done to remove any brown / frosted damaged wood / branches, it also help to keep the plant, either bush, shrub or climber into a manageable shape, lets air into the branches, sunlight onto the branches that helps ripen the wood and buds, and helps energise the plant especially if a feed is given at this time.
Here we grow lots of different flowering climbers and other mentioned types of Roses, but Climbers can be one off flowering, come again flowering and multi flowering as in Floribunda ( bunches of small flowering clusters) these all require different pruning regimes, so it's always good to try hold onto the growers label with the times for pruning and best position ect,
Old English Roses flower only once per year and have the best perfume. Prune after flowering,
Ramblers prune late summer /early Autumn.
Vigorous Ramblers (usually very old type so don't prune so hard) More Modern Ramblers flower best when the new growth shoots from old wood.
Repeat flowering Roses prune Autumn or early spring.
Pillar Roses needs are according to vigour, so prune in Autumn IF growing too tall for the pillar / post it's growing up.
The best way to have really good climber Roses is to control /Tie in as best you can, all the branches / stems as they grow and while still soft enough to GENTLY bend into the position you want, remove any crossed branches at this time, that way it's so much easier to prune and remove and damage.
All these are classed as climbing Roses and all require slight different treatment here in UK.
Hope this helps a bit.
Good luck and have happy gardening year. WeeNel.