No one knows for sure. It's all speculation. The Seven year tribulation is defined in scripture and we know it'll run seven years. Jesus returns at the end or right after that period. I don't know the exact date and no one ones it for sure except the Father.
According to some scholars, Jesus's first coming fulfilled three Jewish holidays in the Spring. Pentecost (festival of weeks) is after these holidays and is the "interruption" between the spring and fall festivals. Pentecost was the day the Church was born. There is some extra-bibicial from Jewish traditions that suggests Enoch was born and taken on the day we know as Pentecost (again not scripture).
If Christ's first coming fulfilled these three spring festivals, there's a good chance His second coming will fulfill the fall festivals. What's extremely interesting to me, is that if we assume Christ will indeed return in the fall timeframe, the AC would have to confirm the covenant some seven years before that (Daniel 9:24-27). Since we KNOW that the treaty is seven years long. If the AC signs this covenant in the fall period (September-October), the 3 1/2 period where the AC defiles the temple (Matthew 24) would put in right around Passover.
Think of it, the newly rebuilt temple is going to have one of it's first sacrifices on Passover in two millennial (the world would be watching), instead of allowing it to happen he stops it and demands the worship himself. Many people would see this and the Jews would realize he isn't their Messiah.
Since we know the rapture is imminent and has no requirements except a specific number (Romans 11:25), I lean that they'll be a gap (probably small one) between the Church being taken and the AC confirming the covenant. Since there's good evidence that this confirming the covenant might happen in the fall, I would say that weighs against the rapture happening then.
I wanted to add another note to my comments. If the abomination of desolation happens on Passover, this day is not in the winter and not on the Sabbath. As Jesus said we should pray for:
But pray that your flight will not be in the winter, or on a Sabbath.