Is it harmful to walk barefoot in the house all day if high arches?

No. If you are equally comfortable without shoes, go barefoot.
Could become painful. People with high arches place more pressure on the bottom of the heels and on the balls of the feet. Waking without adequate arch support could lead to the painful condition of plantar fasciitis.
Yes. High arched feet have less shock absorption and thus will lead to pain on the bottom of the feet. Wear cushioned house shoes with a mild to moderate arch.