Cornus or dogwoods can have beautiful coloured stems during winter and can look stunning when planted with plants which will set off those stems to best advantage. However, the stems you see in the photo below have not grown tall and vibrantly coloured without pruning at the right time of year.
Although it is tempting to cut back everything to within an inch of its life in the great garden tidy up in autumn/winter, Cornus are shrubs which need leaving until the spring. Just before the leaves appear in early spring is the right time to cut their stems almost down to the ground. The stems will then grow quickly and leaf up during the summer. It is only in the autumn once their leaves fall that you will be able to see the glorious, young and brightly coloured stems which have been produced by the pruning you did back in the spring.
So...DO cut Cornus, but only at the right time of year to be rewarded with a show of beautiful stems during winter.