What do you mean by CADPAT? Canadian Pattern? Or are you referring to CADETPAT, a rendition of the MARPAT from the USMC which was phased out years ago? Army, Air and Sea Cadets never wear CADPAT, and as far as I know, do not wear CADETPAT anymore.
At least speaking in terms of Royal Canadian Army Cadets, they wear FTUs and DEUs.
I always wore my FTU and DEU in public if I was going to-and-from parade nights, optional activities, ceremonies and whatnot. I took public transit in the form of bus and train. When questioned about my affiliation, I would simply state that I was a member of the Royal Canadian Army Cadets. I was confused as being a Canadian Army soldier so much that I would have civvies salute me in public and thank me for serving. In these trivial instances, I never bothered to stop and correct them, but if I was in an actual dialogue with someone, I definitely would.
I also never claimed to be higher than the rank I was at the time of social interaction.
The corps that I were in didn't care about the issues which I've described above.
I told other cadets in my corps that I even went home in DEUs on one Remembrance Day, didn't change into civvies and instead went to a local dollar store in my uniform despite this usually being prohibited. None of them cared. The second Remembrance Day parade that I went on, I "stretched" my transportation out by leaving the public parade at the end, walking a few kilometers to a relative's house and finally back to my own house. Again, this time, nobody cared.
I was always told that wearing uniforms in public was prohibited UNLESS used for transporation purposes, tight time constraints and etc. The rules which are in place are there so that cadets can't roam the streets and act like their uniforms are a fashion item, as well as to lounge around in public places in order to casually socialize with civvies.
Civvies and cadets are the same, technically speaking, but I'm differentiating the two here for the sake of clarity.
However, nonewithstanding any of the above, I'm certain that each corps and squadron has different policies regarding public outings while in uniform. I would check with the chain of command if I were you, and if your chain of command is just as dysfunctional as the chain of commands in my corps were, then directly ask a CIC officer.
I aged out at 19 back in late 2016 anyway, so what I've said here may not be applicable to you on that basis alone.
In short, on that note: check with your CIC officers to see what the policy is.