Place the sliced potatoes and parsnips in a steamer (put the parsnips in first where they'll be closer to the hot steam with the potatoes on top since the parsnips require a little longer cooking time). Place the steamer on top of a pot of boiling water and cover with the lid. Steam for about 15 minutes or until the vegetables are tender when pierced with a fork.
Drain the pot and place the veggies in it along with the butter, salt, pepper and horseradish. Mash with a potato masher then add the cream and continue mashing until smooth, adding more cream until desired consistency is reached. Add more salt and pepper to taste. Transfer to a warmed serving bowl and serve immediately.