German here. Yes, they were. The program was called "Erweiterte Kinderlandverschickung".

The Kinderlandverschickung (literally "sending children to the country side") programs were first started before WWI. Various charities organised them, many of them socialist or christian. From 1916 on the national "Reichszentrale Landaufenthalt für Stadtkinder" coordinated everything. The purpose was sending poor children from big, dirty cities to the countryside for their own health, usually during the school holidays for a few weeks. Approx half a million children participated each year between 1918 and 1934.

The Nazis capitalised upon that tradition and in October 1940 the first orders went out to evacuate children into the countryside. First Hamburg and Berlin, later other big cities in the Rhine-Ruhr area.

Older children were either placed into foster careor into camps specifically created for this purpose. Initially it was for 6 months, but this often got extended several times. Young children up to 3, later 6 years were send to the country side together with their mothers and placed with host families.

At the height of the program around 1941/1942 there were approx one million children and mothers staying in the countryside. The official statistics are bit skewed bc quite a few people stayed with relatives in the contryside without any formal arrangement through the organisations.