do i upgrade myself by buying different levels of my main house?
Yes, this is how you would up your level of ranch house. You start off with level 1 of the house style you want, and from there you can upgrade your ranch by buying the next level up. However, you cannot skip levels (You must go from lv. 1 to lv. 2 to lv. 3 and so on).
or do I have to demolish that gold barn (sell all those horses living in that barn first), in order to get a platinum barn?
Yes and no. You do have to demolish the building, however, you don't have to sell your horses before hand. If you sell a barn and don't have enough horse spaces, you'll just become "overloaded" (can't ride, compete, or buy/pick items) until you buy enough barns to satisfy the number of horses you have.