OK, I will be a little more informative. Minnows are naturally coldwater fish, so no heater is fine.
However, without surface agitation (which the filter provides), the water surface will not provide the proper transfer of oxygen and carbon dioxide. Infact, toxics wastes will accumulate extremely quickly and your water will foul.
I don't care how much plant you can stuff inside that 15 gallon tank (which is NOT a lot), they won't provide the necessary oxygen and filtration benefits that a filter can. Let's forget about the fish needing oxygen, beneficial bacterias alone consume a lot of oxygen to convert ammonia into less toxic wastes.
Now, this can possibly be avoided (or at the very least reduced) by providing daily water change, and will the minnows survive? Probably yes. But that's like keeping a goldfish in a bowl and say, "Hey it's doing fine, it's still alive!" Bottom line is, that is NOT the proper way of keeping a fish and a healthy aquarium and non of the inhabitants will thrive.
As for me being rude, that's personal opinion. I'm a sarcastic person (in real life and on the internet), so if I say anything that is deemed offensive chances are I'm not being serious (such as that "those pics are the most terrible pics of the same thing over and over" comment). I'm also very direct, I won't beat around the bush and try to be nice. I've took some seriously horrific pictures, and it's through criticism that made me improve.
I can go on and on but let's get back on topic here.