Frightened of Cheap Chinese Power Supply as I hook up the heated bed
A MK2 heatbed will draw around 12A. The motors and hotend draw only very little power (around 2A, 5A peak), so the 30A supply you have has significant headroom (it is often recommended to derate a power supply by 20%, so a 30A supply would be good for 24A - you're still well under that). It should work fine, even given its dubious provenance.

Winter versus summer should not make a big difference. The largest power draw is during the heat up phase. In winter, the bed will use slightly more power to stay warm, but regardless of whether it is summer or winter the peak power draw during heat up will be the same.

The cheapness of these supplies tends to be reflected in more output ripple (but for heating the bed and running the motors you don't need a very stable voltage) and improper filtering. This may inject noise back into the mains, possibly affecting other equipment nearby. Should this occur, you can just stop using the power supply. However, in my experience, they can deliver the rated power just fine. They're not completely horrible.

Your biggest concern should be whether the wires that lead to your heated bed can handle the current and whether the screw terminals are properly tightened. During the first use, you should check that the power supply does not get extremely hot. If it's so hot it's impossible to touch for more than 1-2 seconds you should not use it.