Here in Luxembourg we have a whole different lot of children's door-to-door begging traditions (some of which have been adopted by adult clubs for fund-raising).
They start on 2 February (Candlemas), which is still always just for the kids, followed by Shrove Tuesday, then the first Sunday in Lent (Buergsonndeg, with a bonfire a bit like Guy Fawkes Day), and finally the three days from Maundy Thursday to just before Easter. This period covers the "hungry gap" in the old (pre-industrial) agricultural year when winter stores were running low. The songs that go with these event often ask for bacon and beans, but the punters are now expected to give (a) sweets or (b) money.
The imagery of Hallowe'en is here too, just like it is everywhere, but I have not seen anyone trick or treating, at least not out here in the country.
At Candlemas the older (11+) kids used to make it a point of honour to be in charge of the smaller ones and not have any adults with them. However, nowadays, even really tiny kids go, so there are some Mums who tag along. I never had any worries about our kids - only about the grumbly Mums (there was always one) who insisted that their kid hadn't been fairly treated in the divvying-up of the spoils.