Last Sunday the padlock on the outer gate was frozen solid, a plot holder who lives behind the site got me in by pouring some hot water on the side of the padlock to warm it up. My sister in law could not get in yesterday morning the key would go in but not turn. I have reported it to the boroughs allotments maintenance company as they have a silicone based WD40 type stuff specifically for locks and will treat it. In the mean time here is a suggestion if you you have frozen padlocks on your plot or shed.
Buy a gel handwarmers that you click the disk and can boil to use again. They are ideal for activating and holding against the padlock to warm it up and melt the ice inside so the key can go in and rotate freely.