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.