Hi Tom W,
The correct way to express this idea is "on winter mornings":
"On winter mornings I sleep in later and don't get up until 10 or 11."
I don't think that the reason you change "in" to "on" is because there's a word modifying it. I can say:
"In the early morning I woke up and made coffee."
The reason it changes to "on" is because we're talking about more than one morning. This is true for other situations where we're talking about more than one morning:
"On Monday mornings I take the bus to work."
"On weekday mornings the alarm clock wakes me up."