If there was more snow and ice on the earth then more of the sun's radiation would be reflected?

Yes this is correct, this is one of the many reasons why global warming would become self sustaining at some certain point.

Glaciers and the Arctics reflect a lot of sun light back to space, which avoids that even more heat from the sun would be absorbed by the Earth.

But because of global warming, these glaciers and Arctics start to melt away, causing more heat to be absorbed, causing more global warming which melts more snow away.

Another problem with this melting is that the melted snow releases a lot of CO2 into the atmosphere, strengthening the greenhouse effect.