Does A Warm or Cold Winter Mean More Late Season Snow?

We hear it every winter after a period of extremes:

"This cold means a rough start to spring".

or..."These warm temperatures mean were going to get a big snow in March".

Is there any truth to this historically?

The first chart below shows some of the coldest winters (December through February) on record in Cleveland and each daily snowfall occurrence regardless of the amount from the 3rd week of February to roughly the Vernal Equinox (March 20th). I didn't use years prior to 1900 as snowfall data is frequently incomplete. The second chart shows the same daily snowfall but for some of the warmest winters on record.

Light blue days indicate snowfall under ONE INCH
Dark blue days indicated snowfall greater than TWO INCHES
Red days indicate snowfall greater than FOUR INCHES

25 days with at least one inch of snow
3 days with at least four inches of snow

26 days with at least one inch of snow
3 days with at least four inches of snow

Bottom line: A very warm or cold winter overall seems to have little bearing on late winter snowfall