Your paragraph correctly punctuated:
I find an airplane's symbolic freedom appealing - whether it is soaring through the sky, industriously filling and disgorging passengers(,) or exultantly defying gravity on take-off, it remains independent and far-reaching in all of its manoeuvres.
In English, semi-colons are only used as a way to separate linked clauses that can't be, usually because the sentence is too long or because a connective is used instead, separated by a conjunction (Example: John is generally a nice guy; however, he can be a bit aggressive, sometimes) or as a means to "break up listings with successive subordinate clauses" . Since the elements "soaring", "filling" and "exultantly" are not clauses but listed elements, a semi-colon here would be inappropriate.
A colon is used before the description of an idea or statement that has been previously introduced to and that needs description but has not yet been described - e.g. "My life is very boring (introduction to the idea): every single day, I get up from my bed, go to school, eat and then go back to bed, and this simple cycle lasts as long as nearly eleven years" - or when the description itself has been introduced to, usually by referring to it as 'the following' or 'this', or other nouns - or sometimes even predicates, such as 'here' ("You can find more information here: blahblahblah.com) - such as 'example' (as you saw me use above) - e.g. "Remember the following: work hard and don't lose faith". Likewise, a colon is used before lists that have typographical supplements that are not joined by a conjunction (Such as bullet points or numbers) or lists that don't obey the main clause's noun casing (for example not embedded quotes) In your case, however, the idea is neither being described nor is a noun-case-disobeying list, but is rather being explained or elaborated on (as we can see by the use of a conjunctive - "whether"). For explanation, justification, elaboration, clarification or expansion, we use a hyphen (-).
Finally, if you feel really smart, you can put a comma (they call it a "serial comma") before "or": it is usually unnecessary, but most educational sites tend to use it.
EDIT: I just realised the 'whether' bit was actually a dependent clause and part of the description. Then, yeah, you can leave the colon as it is - it's fine.
