SEEDS

One of my books, Mathew Biggs's Complete Book of Vegetables, says to sow under protection (cloches/fleece) or you can grow leeks in a cool greenhouse in trays/pots/modules of seed compost. Pot on the seedlings spacing them 2 inches apart when 2 true leaves are prduced or when they begin to bend over. Harden off before planting out in late spring. "Although all varieties are suitable, later sowings of mid-season and later types are particularly successful in seedbeds." Also says to warm the soil before planting out, using black plastic or cloches.
For broccoli, it says to sow in situ from mid to late spring so maybe you can hold off on planting those seeds until the weather improves where you are? It does mention sowing in seed trays but only for early spring crops and to do so in late summer/early autumn.
Carrots I think you just have to wait with too. You can't transplant them; same goes for most root vegetables.

It appears to be snowing here so my plans for sowing this afternoon, while I wait in for a gas engineer, look dashed. I'm banking on everything catching up when the weather improves a bit. I'm glad I put some fleece on one of my beds - only peas in there so far but I want to put onion sets in as soon as work and the weather permits.