I never cut my perennials back until spring--something I learned from Ken Beatie from get growing--The plants sticking up collects the snow and that gives protection to the roots.

A good rule of thumb is if you are unsure about a plant needing winter protection is to give a good layer of mulch to the roots anyway. If it would do with out it it will be better with it and if it needs it it's got it. I mulch all my perennials.

Not sure about the first one but blanket flowers and Veronica are pretty hardy.

Yes I mulch all my plants for winter and leave it there though summer too, breaking down an providing much needed nutrients. It is like the forest floor ;) There is the idea that leaving the stalks can harbour pests in them. That is a yes and no thing I think... since they could hide in the mulch anyways. Speedwell does alright here in zone 2 blanket flower is actually a bi-annual and does well here z2 and reseeds itself. Rumex sanguineus I think is z5-6 so is not so hardy for colder zones.

This is just a "heads up" to say that I have grown several different gaillardia cultivars including Arizona Sun and have found that most overwinter fine and live for several years with minimal care. However, I have purchased and planted several plants of Arizona Sun over the last 3-4 years and found them not to live long for me. Maybe it has more genes of the annual gaillardia species. Goblin, Burgundy and some un-named ones do much better in my garden.

I usually cut all perennials down in the late fall. I do leave 4 - 6 inches of stem, just to trap the snow for more insulation. In the spring, I don't have to walk on the saturated soil to clean up. Works for me.