We've gone in both ways - Snow Lakes and Colchuck. We've always gone in and come out the same way however. Sounds like you are prepared to do the loop. Personally, I would choose to go in Colchuck. You'll have about 4 1/2 miles and 2500 ft of elevation to the lake, and 1st night's camp. The next day you have Aasgard to go up but is not near as bad as you might hear. Its about 1 to 1/12 miles and 2200 ft but once on top you've done all the vertical you'll need to do. The rest is downhill. If you plan on staying just one more night I would recommend camping at either Leprechaun or Vivian. We usually camp in the first trees you come to after Aasgard which is just above Inspiration lake - beautiful place to camp. But if you camp there, you will have a long slog out the last day, so you're better off going further before camp. Also, the drop from Vivian to Snow Lakes can be dicy if its wet out. You'll also need pretty good balance to cross the outlet of Vivian (which you'll have to do whichever way you go).
Going in the Snow Lakes route is about 6.5 miles and 4100 ft - can be long, hot and dry. Scenery to Snow lakes I think is much better than the scenery to Colchuck until you start up Aasgard. Once at Snow Lakes you'll want to camp. The next day you have "the Wall" to look forward to - about 2-3 miles but the 1300 ft of elevation gain is all done in the last 3/4 mile. Honestly, I prefer going up the Wall to coming down it (a little safer I think). But if you do the loop you'll have to take the good with the bad - either climb hard for two days to Aasgard then downhill from there (including down the Wall) or, climb hard for 2+ days, including up the wall, then more uphill to Aasgard. Pick your pain.
Lastly, if you really want to see the Enchantments, you need either more days or more hikes. With just three days you'll be limited on what you can see and do once on top. As I said, we camp above Inspiration after coming up Aasgard. This camp is fairly central to the majority of the Enchantments area. You can dayhike up Little Anapurna from there, dayhike Prusik Pass and beyond, dayhike down as far as Vivian if you want, then back out Aasgard and Colchuck.
One last thing - have you got your permits? If not, you better show up at the Leavenworth Ranger station at 4 or 5 AM the morning of your hike to try and be sure to get permits - they only reserve a few for "drop-ins".
Here's what I would suggest if you are only able to camp two nights:
after you get your permits drop off your first car at Snow Lakes trailhead
and head to Colchuck trailhead. Camp at Colchuck the first night. Go up
Aasgard early the next morning, once on top you can liesurely hike on down
to the lower Enchantments, seeing the sights on the way. You might even
want to throw the packs off and go up Little Annapurna before heading on
down to the lower lakes. Throw the packs off again at Reflection lake and
buzz up to Prusik Pass. Head on down to Leprechaun or Vivian and camp the
second night. Head down the Wall and out Snow lakes the last day. Believe
me, doing it this way will be alot easier on you than doing it in reverse,
and you will have the energy to do the side trips I mentioned. Doing it
the other way you will likely not have the energy to do the side trips as
all your hiking the second day is all uphill.
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A family of Mountain Goats.