Learn English – “I mind to” vs “I am minded to”

Close-minded was first, but closed-minded is dominant:

Here's the earliest close-minded reference I can find from a Narrative of a Journey in the Interior of China, by Clarke Abel, 1818:

I found closed minded back to 1913 in The Century Magazine:

Edit:
After considering @FumbleFingers' comments here and his subsequent answer, I have to agree that most of the earlier close-minded references found through Google Books (including the one above) are using close |kloʊs| in this sense (from NOAD):

• not willing to give away money or information; secretive : you're very close about your work, aren't you?

This is also proven by this definition of uncommunicative from John Craig's A New Universal Etymological Technological, and Pronouncing Dictionary of the English Language, 1859:

It seems the phrase was once a common description for someone who "kept their own counsel"—usually used as a derogative, but sometimes as a compliment.

However, I did find this earlier use of close-minded specifically to mean the opposite of open-minded from an 1898 issue of The Outlook:

I also found evidence of a shift towards this sense of close-minded in other writings by the early 1900s. So, to conclude, I think the only thing new about the confusion evident by the 1960s was the frequency of the two terms in print. I realize this may not ultimately answer the question, which is correct, but the timeline seems significant to me.

Longman is generally correct. "Spring to mind" can be used whether the speaker is talking about their own mind, or someone else's.

"Does anything spring to mind?" (The mind of the addressee is understood.)

"Nothing springs to mind." (The mind of the speaker is understood.)

The alternative is far less frequent, but does still occur. I notice that most recent example in the OED is this:

1991 G. Carey I Believe (BNC) 74 Let me tell you of the images that spring to my mind when we talk about water.

I would say based on historical and current practice, that it is best to follow Longman's advice and avoid the personal pronouns. If the meaning of the phrase is ambiguous in a particular context without the personal pronouns, I'd consider eliminating the phrase before using the pronoun.