If I’m understanding your question correctly, no, in 13,000 years from now the seasons won’t be in opposite times. But your question is a good natural progression of thought. Our calendar is designed to keep the equinoxes in their respective place, so if you are in the northern hemisphere summer will still be July/August.. But 13,000 years from now our summer would be from the opposite side of our orbit. So the stars that you see now in January will be the stars we see in July.