Longmont claims the power to prohibit open carry in parks (the ordinance actually prohibits all weapons, but it's clear that they can't prohibit concealed carry). The state statute that allows any city to ban open carry on city property requires signs at all entrances in order for them to prohibit open carry, but that park (and most, if not all parks in Longmont) don't have entrances -- they're open on all sides, so it doesn't seem that they can really prohibit it.
I asked the City Attorney specifically about this, and he says the City has the authority to prohibit open carry because it's a home rule city, as is Denver.
Honestly, I doubt if you'll have a problem, but you should be aware of the City's position.
Edit: To clarify, this is city property.