Which test for hierarchical within-between design?

Hi everyone,
I'm about to design an experiment with one independent variable of three levels. However, two of the levels can be 'grouped together', and I'm quite unsure about if my experiment design makes sense, and even more important, which statistical test I can use for evaluation.
For simplicity, assume the following analoguous experiment:
Participants shall rate the likeability of animals (animal = independent variable). There are only three categories of animals to be rated: cows, green horses, and red horses. In this example, I would want to answer two questions: (1) Are horses preferred over cows? and (2) Are green horses preferred over red horses.
Also, I want to directly ask questions about the comparison of the shown green horses and the shown red horses.
But, I do not want the participants that saw the cows to see the horses and vice versa. Thus, I plan to do an experiment where I have two participant groups (in-between design). One group sees only the cows, the other group is assessed through an within-subject design where it first sees one type of horse, assesses it's likeability, and then sees the second type of horse and assesses it's likeability.
For research question (2), I would use the results from the within-subject design, whereas for research question (1), I would like to use the in-between design, but this is were I struggle: Is there a way to somehow "merge" the red and green horses ratings, so that I can compare them in a correct way with the ratings for the cows?
Does the experiment design make sense for such kinds of tasks? Is there a common test that models that type of hierarchical structure? I was thinking of mixed ANOVA, but I'm not sure if this will work, as it's mainly designed for the within-subject part being a repeated measurement, thus occuring in both groups of the in-between part..?
I would be really happy if someone could help me with this :) Have a great day!
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