Do not expect all 4 seasons. We usually skip fall all together or have a few weeks of it. Spring starts in mid March and goes through May. It is common to have several days in May in the high 90's and maybe 1-2 100 degree days. So Summer is from May- Halloween. Fall if we get it is from Oct.31-mid December. We do start winter in Dec but we can still have 70 degree days. January is the big winter month but we can still have 70 degree days and the have snow the day (it does not stick). We received close to a foot of snow this year and it was the first time in 20+ years. Most years we only get 1-2 days of snow and it melts within hours. I have lived here 25 out of my 29 years of life. You get used to the weather and know not to invest much in winter clothes. :) It rains alot in April and May. It is not uncommon to have a drought July-September. Don't expect several trees to change colors in the Fall. A few do but nothing like the North.
Richardson is a suburb of Dallas just north of Downtown. Thus weather here is typically same as Dallas area weather. Hot and humid summers .... Somewhat cold in winter. I say somewhat cold, because we moved from Michigan and we do not find it cold here at all. But that is not true for friends that grew up here.
Rest of the time in the year, it is pleasant.
Snow it does ... but not a very common occurrence. Last year, we had some snow ... But the snow generally melted in a few hours. Only one snow was bad and took a few days to melt. But these are rare and happens once in 10 years as I was told.