I like to make yogurt from heavy cream so when it's frozen, it keeps creamy texture when stored in the freezer in several days. Do you think this works? Does high fat content affect incubation process of yogurt? Should I use heavy cream or half heavy cream half whole milk?
This is a very normal thing to do. The result is not called yogurt, but sour cream. You can use yogurt, especially lactobacillus yogurt, as a starter for full-fat sour cream of the Eastern European type. The fermentation process is the same as for yogurt. It gets a very nice characteristic smell which is different from that of yogurt. It might stay slightly soupier than yogurt, even after sitting in the fridge, that's normal.
There is nothing special you need to consider, just go ahead and make it.
You can add cream to milk when making yogurt. This will increase the fat content. However, if by "creamy", you are referring to texture of your yogurt, there are other variables that contribute besides fat content. See this question, for example. Also, there are variables besides fat (sugar content, for example) that influence the texture of frozen ices.