Yes, the counter will remain.
From the Comprehensive Rules:
121.1. A counter is a marker placed on an object or player that modifies its characteristics and/or interacts with a rule, ability, or effect. Counters are not objects and have no characteristics. Notably, a counter is not a token, and a token is not a counter. Counters with the same name or description are interchangeable.
You can put a counter on any object on the battlefield, as long as that object is a valid target when the ability/spell that puts a counter on it resolves. You can only put a +1/+1 counter on Riddleform using Hadana's Climb's ability if Riddleform is a creature, but any +1/+1 counters already on it when it stops being a creature will remain. It's worth noting that, since +1/+1 counters only have an effect on creatures, they'll essentially do nothing while Riddleform is an enchantment.