SNS3
Myself and plenty of other instrument rated pilots would definitely pay for a 1-day course on how to interpret these (and other) diagrams. Do drop me a line if you know somebody who can do one, in southern UK somewhere.
I fly a nonpressurised non-turbo plane with a ceiling of about 20k feet i.e. about 500mb, and not really de-iced either.
European airway MEAs are high enough to place you into icing temps most of the year, so flying below cloud is usually not an option - unless you go VFR and then you have the usual scud running scenario, etc.
So, the strategy in IFR flight planning is to find VMC on top, and find it fast, and stay up there for the whole flight.
It's actually not much different for a fully de-iced plane; not many of them can sit in mod ice for 5 hours, and not many passengers want to sit in IMC for hours, puking up.
The particular use of a skew-t (or tephigram) in this scenario is to find how high the cloud tops are likely to be along the route. One then files the flight plan well above that level. During the climb to the FP level, say FL160, if you find tops at FL100, you ask for a stop climb at FL110 and that gives you a better speed (unless you have a tailwind in which case you may want to go higher) as well as conserving oxygen.
This data was not available a few years ago. Pilots would climb and hope for the best. In N Europe, cloud tops are rarely above FL160 unless there is some "vertical development" going on, and then all bets are off; FL250 is common.
That Unibas site uses (I believe) mostly GFS data, and somebody clever can work out cloud tops from GFS directly, e.g.
this.
Sorry if a couple of URLs got merged in my previous post above...