Those dates, in the Northern Hemisphere, are considered the start of our four seasons. April won't necessarily be warm, however. The trend in the Northern Hemisphere now is warming (cooling for my Australian and NZ fans!) but depending on your latitude, proximity to the ocean, and other local factors, it might not be very warm yet as spring technically arrives.
|From Wikipedia, Season article|
More goes into starting the warming of spring or the cooling of autumn than mere minutes of sunlight. Atmospheric realities delay heating and cooling, insulating the surface of the world, in effect. So, if the date in the Northern Hemisphere with the most sun is June 21, you might wonder why that isn't the hottest day of the year. It usually isn't. Hottest days are usually in July or August. In San Francisco, because of the influence of the ocean, the hottest day is usually around September 25, after astronomical autumn begins! (This results in an interesting non-atmospheric phenomenon where tourists arriving in June, expecting summer, freeze their bums off, and sweatshirt vendors on the street make a bundle of money selling clothes to them. :D ) In Southern Arizona, years when there's a good monsoon---a season of rain, with clouds coming in by noon most days--June actually is the hottest month, for the cloud cover makes July and August almost tolerable.
Again, the sunniest day of the year in the north is June 22. Interestingly, the closest the sun and earth draw to each other is in January, as the illustration above shows, so the summers in the Southern Hemisphere will be a little hotter, all other matters being equal.
The atmosphere takes time to warm, and the ocean takes longer. This is why San Francisco's seasonal lag is greater than inland lags, and it's why the peak Northern Atlantic hurricane months are September and October, when the ocean has finally warmed up to its summer temps.
Historically, some cultures have named six or eight seasons, not four. Other planets have longer or shorter seasonal lags. Mars's is almost zip! (It has very little atmosphere.) Uranus, on the other hand, has over a hundred years of season lag (data nmsu.edu):