You don't say which variety of Solanum they are, some are only just frost hardy, and a standard is particularly vulnerable in winter, so it may be wise to move it somewhere very sheltered or give it protection.

Now is not the time to prune them - regarding the climber, hard prune in Spring, once the weather's warmed up a bit and growth has started. You can trim off surplus, wayward shoots in summer. With the standard, clip to shape in Spring, if the topgrowth has survived the winter.

The standard could be Solanum Crispum which is probably the hardiest Solanum. I am growing Solanum laciniatum this year (lovely big leaves and small purple flowers - but not hardy alas). Bamboo has given the right advice about the time to prune. No idea about the climber (my guess is that frost will also nip it, so best to leave pruning till spring).