Officially Midsummer Day is 24th June.
But we don't have a Midwinter Day.
If we did, when might it be?
Midwinter is today.
If you take winter to be 1st December to 28th February, i.e. meteorological winter, then today is the middle day of the season. We've already had 44 days of winter and after today we still have 44 days to go, so we must be halfway through. Things aren't quite so clear cut in a leap year, but it isn't a leap year so midwinter is today.
And midwinter is also 4th February.
The astronomical definition of winter is the period between the winter solstice and the spring equinox. Winter is 89 days long so we're looking for the 45th day after the solstice and that's 4th February. Technically the solstice moves around by a few hours every year so sometimes the halfway point is on 5th February instead. But whichever day it is, 4th or 5th February, the bad news is it's still three weeks away.
And midwinter is also the day after tomorrow.
I'm basing this on temperature because it would make sense to think of midwinter as the coldest part of the year. Clearly this varies from year to year so the trick is to average out a lot of past temperature data and see where the coldest day is. I found a dataset for Oxford with a daily record going back over a century, so have been able to calculate the average maximum temperature on every date from 21st December to 6th February. Here's the graph.
The average maximum temperature in mid-December is about 8°C. It falls to about 7°C by the start of January and fluctuates around 7°C until the end of January, after which it inexorably rises. The coldest week in this dataset is 17th-23rd January and the day with the coldest average is 17th January, suggesting 17th January is the height of midwinter.
And midwinter was also 21st December.
This is because 21st December was the winter solstice and by definition the winter solstice has the minimum number of daylight hours. It's seemingly weird that temperatures continue to fall for four weeks after minimum daylight but that's because the land and sea are still emitting heat absorbed in the summer.
So take your pick as to when Midwinter Day falls, but it could be last month, it could be next month or it could be right around now.
21st December - minimum daylight
15th January - midpoint of meteorological winter
17th-23rd January - coldest daily temperature
4th February - midpoint of astronomical winter