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.