You have to go by the weather rather than calendar month. For scarifying, the lawn needs to be dry - if you go at wet grass (especially with a powerful electric machine) you're going to mostly be pulling it out of the ground at the root.
Better to wait until it gets a bit warmer when the grass has dried out from the winter and, crucially, is growing again. Also, keep your eye on the forecast for the days after and try to time it to coincide with rain to help the recovery.
April's usually a decent bet in the UK. Wait for a period of dry weather followed by wet, and time the scarification for the very end of the dry bit.
Australia is home to the Gympie-Gympie which has nettle like barbs so venomous that the pain from the sting has lasted for weeks (up to a year) and has been said to lead to suicide.
I have a garden now. When we moved in it was in an absolute mess. We left it for the first year, then a friend who's a gardener did a complete revamp on it during February - cost quite a bit even at mates rates. We've now got a patio and a nice lawn and sleepers and edges and stuff. But 3-4 times over the last month, ever since he's done it, we've had a fox digging up huge patches of the new turf every few f** days. I've bought sheets and pinned them down over the grass to try and help it bed in without it happening, but one of the edges was loose last night and now it's all ripped up on that corner again. Cunt. Think we might need to buy one of those sonic deterrent things, but I've been trying not to as it'll presumably distress the new (and local) cats.
Killing the fox is illegal it seems.
PS: Just recalled I may have already posted about this but meh. It happened again last night hence the vent.
Stick on a kimono, club it to death with a baseball bat and claim the Jolyon Maugham defence.
(Bearing in mind his Good Law Project invariably loses in court).