I have a similar situation running to my barn. We ran 10/3 with ground in UF. I would have run 6 or 8, but we got a great deal on the 10/3.
We will be putting a panel out there, soon.
We also have a 30A breaker protecting the UF and the barn.
Remember, the breaker protects the downstream equipment.
One issue you will have: I can't find a 110V receptacle that will accept 10 guage wire. You will need a pigtail or something to convert.
Also, each leg (not technical, but I am going to talk color) will allow 30 amps. That means the red will do 30 and the black will do 30. If the heater is really drawing 23 on 220, then both the red and black are already using 23A. Note that the label is for the maximum, not what it truly does.
That means you can have two 110V circuits that can supply 7A per--assuming the heater is running and drawing 23A.
Also, I certainly agree with the other posters who like the sub panel idea.
Also, I agree with the person who said that sometimes appliances are expecting to be protected with a 15A breaker, so they could burn up using your original plan. Solution: buy an inline (comes in various ways including power strips and extension cords) 15A breaker.
I hope I helped.
By the way, I am planing to go with the flexible conduit with wire already in.