Am I sowing first early potatoes too early?

I work in a school garden. Because the children get holidays at the end of June, we try to sow the chitted seed potatoes by mid March at latest. This year Easter hols are very early so we probably need to sow next week. With the bouts of frost and cold….Is this going to affect the potatoes in the ground or will they just start growing in the soil when temperatures start rising. Ideally I would like to leave sowing them until until slightly later in March…..last year with late harsh frosts… I had to cover foliage as it appeared.