Yes, but it's hard to predict when and how we might get it. Winters in the midlands in the UK are a bit hit and miss on the weather, sometimes if there's going to be a cold snap it comes early in the autumn/winter (November or early Dec) or sometimes late. Often it's just a light dusting of snow over a few days, but there are occasions where it is several inches deep and lasts for a little while. Usually not more than a week or two though.
As a child, school closed on my birthday at least once, which was lovely. My birthday was usually in the half term holiday in February, but occasionally it fell on a school day. One of those was a snow day so I didn't have to go. It also sometimes snowed on my sister's birthday in November. In my memory I can remember snow as late as April, including heavy snow, but usually that means we haven't had any here prior to that. Other parts of the UK are different though and London it's quite unusual to get a lot of snow. It creates utter chaos in the capital when it does happen - I had to teach there one year during a snowstorm and all the tube services were out because of frozen points on the overground sections.
My parents say it once snowed on my Mother's birthday in June, but that was before I was born.