My immersion chiller is a 40 foot one. I get down to 65F in about 15 minutes in the summer. I can get down to 55F in about 20 minutes on very cold days in the winter. I'm a stirrer, but.........
I'm careful about stirring, so that I don't oxygenate when the wort is still warm. According to Palmer and others, the cut off point where you go from oxygenation (bad for the wort) to aeration (good for the wort and yeast) is 80F. Whether this is accurate or not for a cut off point I don't know, however it is what I've read and heard for many years and I follow it (for the most part).
My wort tends to drop down to about 120F fairly quickly, but at that point the cooling rate starts to slow down, so I do start to "very gently" stir. I also put my stirrer spoon into the wort at the end of the boil, so that it is sterilized by the boiling temperature wort, and then when I'm ready to start stirring I don't have to worry about contaminating my wort with an unsanitized or unsterile stirring spoon.
When my wort is above 120F, I might take the spoon and very gently coax my wort into a movement around the boil pot, just to get the cooler wort near the immersion chiller blended into the hotter wort away from the immersion chiller. I'm very gentle when I do this and only do it about 2 or 3 times, as I don't want to prematurely oxygenate the wort. My goal when gently stirring 2 or 3 times above 120F is "do not create any bubbles"!
Once my wort is down to 120F, I start to gently stir consistenly, but slowly (still avoiding any bubble creation!). I gently stir constantly from 120F down to 80F.
Once I get to 80F, I get aggressive with my stirring, creating bubbles, foam and getting a real nice whirlpool going. If the wort temperature seems to have stopped dropping, I'll stir briefly in the center of the immersion chiller (the wort in that area usually isn't moving much and I get a temperature differential between the outside of my boil kettle and the area inside of the wort chiller. The occasional quick stir in the middle of the wort chiller, blends the two different wort temperatures together.
Once I'm down to within about 4 degrees of my intending pitching temperature, I turn off the immersion chiller and pull it out. I then stir aggressively to get a nice whirlpool going for about 2-3 minutes. I then let my wort sit and settle out for about 5 minutes, with the lid on (the lid is on just to keep airborne contiminants from settling on my vulnerable wort. This last whirlpooling stir concentrates my break material and any hop bits in the center of the boil kettle. My drain pick up is on one side of the boil kettle, so that when I start the transfer to the fermenter, I can leave the break material and hop bits behind.
Once my wort is in the fermenter, I give it 30 minutes of aquarium pumped air through a sanitized aeration stone. I then pitch my yeast, attach the airlock and let the yeast do their magic.
ps.
On a side note, if you look closely at your boil pot in the snow bank, you can see that the snow on the sides of the boil pot has melted away, leaving an air gap. This air gap is heated by the hot kettle, so the snow isn't against the boil pot, but instead heated air is against the boil pot. This is why open air is quicker than in a snow bank.
My customers (I'm a bearing engineer), sometimes seek advice on cooling bearings down to -65F for installation into wheel hubs, etc. Through testing, our research has found that the cooling of the steel is not as quick as you'd expect when the bearing is packed in dry ice, because of the air gap created by the warm bearing, as compared to -112F dry ice. We tell them to gently drop the dry ice into anti-freeze to super cool the anti-freeze down to -55F. Still a liquid at this temperature, it stays against the bearing and quickly cools the bearing to -55F. Of course, we can't do that when chilling our wort, as the anti-freeze/dry ice mix boils violently, splashing around and would contaminate our wort with anti-freeze that would kill us if we drink the beer cooled in this manner. I just wanted to point out how I know about the effect of a solid, extremely cold material melting and creating that warm air gap that inhibits cooling of the container that it is set down into.