I'm not sure if you can say that March came in like a lion or a lamb. Compared to the winter we have had so far, the first days of March were relatively lion-like. However, if you look at past winters, it is more like a lamb. I guess only the end of the month will tell, that is if you believe in things like this that supposedly predict the weather and other events.
Coming in like a lion and going out like a lamb is a form of adage or proverb. There are a lot of things that people believe when it comes to predicting weather. Some look at signs on animals, in nature or rely on the moon or stars.
When I look up the definition for adage it says "a pithy saying, proverb or old saying." A proverb or lore is probably a more appropriate term for weather related beliefs that date back several years.
For centuries, shepherds and sailors, people whose lives and livelihood depended on the weather, relied on lore to foretell tomorrow's weather. They showed a keen sense of observation and quickly connected changes in nature with rhythms or patterns of weather.
Some weather proverbs are nothing more than rhymes or imaginative contradictions such as the March lion and lamb lore. Others have survived the test of careful observation and scientific reasoning and become reliable guides to weather change.
Those sayings that prophesy daily change, usually pertaining to sky appearance, cloud movement or wind change, have documented success. For example "When stars shine clear and bright, We will have a very cold night" or "Red sky at night, sailor's delight; Red sky in morning, sailor take warning." Another one "chimney smoke descends, our nice weather ends" makes perfect sense since the smoke will not rise if the air is heavy with moisture. Also a red sky means rain or dry weather according to the time of the day it occurs based on certain optics and conditions of the atmosphere. As Minnesotans we know that "the squeak of the snow will the temperature show" because very cold temperatures make the snow harder and "crunchier."
There are some proverbs that, in my opinion, have no real basis. "When the wind is in the east, 'tis neither good for man nor beast" is one that many people use when it comes to fishing but I can't see how it can affect animals much less people. Another "when chairs squeak, it's of rain they speak" can be taken different ways because we all know chairs can squeak just because the wood is getting dry and needs oiling.
Could it be so far off to think that weather at the start of the month will be the total opposite as the weather at the end? No matter what the proverbs say, I would like to interpret the weather at the start of this March as being more lion-like just so that we can hope for a lamb-like end and the start of a beautiful spring.