"Why are you looking for this horse?"
Translation:Dlaczego szukasz tego konia?
Yes, you could say this. Ten/ta/to are masculine/feminine/neuter for 'this'.
'Tego' is Genitive for both masculine and neuter, and also Accusative for masculine personal and animate nouns.
Here it is in Genitive, as 'koń' is masculine and szukać (szukać kogo? szukać czego? to seek whom? what?) takes Genitive.
Check the full declension here.
While I admit I didn't look at the lesson notes beforehand (that's my bad), I did not find out until later lessons that szukać takes genitive because there are no practice sentences in this lesson that have anything other than masculine animate objects which are gonna be genitive no matter what verb is used. Maybe throw in a couple of feminine ones just to make that crystal clear? :)