In the Coptic Church the Trisagion does in fact change from season to season. Annually(also during fasts) Its Holy God, Holy Mighty, Holy Immortal, who was born of the Virgin, Have mercy upon us. Holy God...Who was crucified for us, Have Mercy upon us. Holy God...Who arose from the dead and Ascended into the Heavens Have mercy upon us.
On the feast of the Nativity and the 2 weeks that follow, the First verse is only said(3 times). During Holy Week, the second verse is only said. During the Feast of the Resurrection and the Holy 50 the third verse without the part mentioning his Ascension and after the feast of the Ascension the whole verse is said.
This Verse: Holy God...Who was baptized in the Jordan, Have mercy on us. Is said only on the Feast of Epiphany. Other than these 4 occasions All 3 verses are said.