Perennial Herbs in Containers for Cool Room

I am interested in raising some container herbs for my room this spring and into the future, particularly in perennial varieties that can withstand cold (I am in USDA hardiness zone five, and often leave the thermostat at 55F/13C in the winter) and mild drought.
At the moment, I have containers with spearmint and chives that seem to be stagnant, but typically come back in the spring/summer. I was looking at sweet woodruff and wormwood, and any suggestions you could offer would be most appreciated (it is not required that they be culinary).

You don't mention light, but because chives and mint seem to work in your room I am assuming that the light is adequate for other herbs that can tolerate some shade. Sweet woodruff, certainly, should behave much the same way as chives and mint, going stagnant or even dormant during the winter months and bouncing back in spring. Sweet woodruff is also compact enough to do well in containers. Wormwood is a bit more complicated because there is a range of heights and because they like more light. So long as the plants do not freeze solid in winter, tree wormwood is a very nice subject for a large container. Despite its name, it does not get more than about 4-5 feet in height, and it can be trimmed back from time to time to keep it manageable. But many people, especially immigrants from North Africa like to grow it as a container plant for its silvery leaves, miniature tree-like look, and for use in medicinal teas. The common wormwood (Artemisia absinthium) is probably too gangly to grow indoors in containers. Shorter varieties such as roman, Silver Mound, and fringed wormwood may do well in containers, but like chives, mint and woodruff, they will likely slow down and evern go dormant for a while during the winter months.
The choice of herbs for container culture is mainly dictated by the compactness of growth habit and the tolerance to lower light. Light often turns out to be the limiting factor for indoor herbs. But your conditions of cool temperatures (10-15 degrees Celsius) and mild drought are actually very beneficial for herbs during the months when light levels are at their lowest. These conditions help slow down the rate of growth so that the plants do not starve themselves to death during the period when they don't have enough light to make food by photosynthesis.
With these points in mind there are probably many other herbs that you could consider. Certainly I would look at herbs such as scented geraniums, thymes, savories, oreganos, sages, lavenders, rosemaries, and others. Some herbs you probably won't have success with in the winter months are basils and the sensitive and fast growing annual herbs such as dill, coriander, and chervil. Basil needs more light, heat and water to do well while dill, coriander and chervil need more light and water.
Every growing situation is different and it takes some experimentation to find the right plants. Don't be surprised if some of my suggestions above don't work out for your particular conditions and needs.