I know someone else said to 'not cover your pot while boiling.' I agree in general that is good, but if you are going to let your pot sit for a bit, you need a sanatized cover for it for then. I usually do that by putting my lid on loosely and letting the steam of the boil sanatize it, but you can use starsan or idophor.
Since you don't have a chiller, I strongly recomend a sanatized lid, even more if you are going outside with it. While there is probably less airborn bacteria, there is greater chance for particle (tree branches, leaves, stray dog, etc) contamination.
I also agree your sink or bathtub would be better to cool it in, water is about 1000 times as dense as air, so it has at least that much more capacity to take away heat. If you use the water in freezer method, you need to have cleaned water for that - boiled and put in sterilized container, or fresh from the store in sealed containers. If you still want to go outside, get a tub of some kind that can holdyour kettle and fill it with water before you start brewing "Why?" you ask? because it will cool to about 32 or 35 while you are getting your boil going and help remove that temp faster than outside air alone, if you just put it outside, it might not be cool enough to pitch for 5 or 6 hours, air heat transfer is wickedly slow. I know I had a must that was to warm and needed to cool for like 5 hours, granted the inside was at 80, but the must started at like 95, so it was 5 hours for about 15F
Sterilize v Sanitize. These 2 words have specific meanings and one basically said all or almost all are killed and the other says enough are killed. In brewing we sanitize trying to get enoughed killed so that the yeast have the upper hand (by like 1000 to 1). Why don't we sterilize everything well because it costs to much. Sterilizers cost more (stricter standard) and are harder to use costing more time. As the pot gets sterilzed by the boil eventually, no need to treat it before hand, just everything that will come in contact with cool (below 150-160F) wort.
I keep a container of mixed up sanitizer and hit my hands and tools all the time over and over again during the boil and make.