UPD. Actually, you are free to use adjectives in any order. It depends on what are you going to put the accent on. For your example with the lovely old red post-box you may say "чудова/мила стара червона поштова скриня", "червона мила стара скриня" or even "чудова червона поштова мила скриня". It would sound somewhat weird.
Basically, you should use the order as in yours example, but it is not the mistake to shuffle adjectives according to your language tastes
Old answer: In the Ukrainian language you are not stuck with a defined order of words. It is up to you how to use it. But in the official documents and letters you ought to use the direct order (it is similar with English). You can read more on Pidruchiki website here about the sentence ordering.
Up to your questions, such words as "to my mind", "in my opinion" etc. can be in any part of the sentence as well. Each of them is so-called parenthesis, you must separate them by comas. Further reading
So, to summarize, you are allowed to say "In my opinion, it was cold yesterday" like following:
"На мою думку, вчора було холодно"
"Вчора, на мою думку, було холодно"
"Вчора було холодно, на мою думку"
Well, the last one is used rarely. The first and the second are almost equal in usage.