I would like to combine a trip to Hong Kong with hiking some of the islands' trails. What is the best season for this type of activity in that geographic region? For instance, it should not be too hot (nor too cold) and there should be little chance of rainfall.
Anytime between May and October is hot and humid. Depending on your tolerance to heat (and especially humidity), May and October could be fine. But summer in HK is long, and usually newcomers are miserable the first few years... August is typhoon season. June to September, it takes the A/C on non-stop to dry clothes.
Winter is short and, despite locals wearing parkas as soon as temperatures dip below 20°C, pretty mild. We're having a few cold days now – 8~11°C – but that'll pass soon enough. By the end of the Chinese New Year festivities, spring will be here. The "winter" and spring months are usually quite dry.