Good question. Late answer: I don't think it does. It could imply that, but it really only means that you should "experience spring" in Stockholm. It's the kind of thing you could see in a travel agency ad, where they might offer you to book a trip to Stockholm in the spring. You might book your trip in December, when spring definitely hasn't arrived yet, and only travel here in May when it has.
Not you, it makes zero sense in English, even in a travel context. A travel agent might use 'Enjoy Spring in Stockholm' or 'Visit Stockholm in the Springtime!' but this? Pah. No way. This only works where 'spring' is a person i.e. Meet Bruce Springsteen in Stockholm. That makes sense. Otherwise, no.