2nd Edit! Modified my answer about semi-conductors based on jk's answer below, read the history if you want to see the wrong bits I modified!
Everything gets weird within certain limits. I mean, sure, the resistance improves in conductors but it increases in semi-conductors, and that change effects how the IC works. Remember that the way that transistors work on the basis that you can modify their resistance, and if the temperature drops so low that you can no longer decrease their resistance, you've got an issue! Imagine that suddenly your semi-conductor essentially became a resistor... how do you control it? It no longer behaves the same way! Now I'm a bit confused at where you're getting the -25°C, as the industrial/military spec should put it at -40°C for the minimum operating temp.
But for the space question, I can answer that as I work in a space lab! In general you have three thermal concerns in space:
1) In space, you only radiate heat. Radiation is a terrible way to get rid of heat. In the atmosphere, you conduct heat into the air around you which makes cooling a lot easier. So in space, you have to put big heatsinks on to get the heat into larger radiative surfaces.
2) If you have a component which doesn't generate heat, then space is happy to let you get really friggin' cold! In general, what you do is you have active heating elements to keep components which don't generate more heat than they radiate but have thermal limits.
3) Heat swings are common because you will exit and re-enter the sun's rays. Thus you need to have active thermal management where you have a big heatsink which can radiate heat when it's hot, and a heater for when it's not.
You can also get extended temperature range devices which go lower and higher, but there's pretty much always a limit. Some of them are for where the cold temperature will crack the die because the metal will shrink more than the plastic (or vice versa) which is why they list limits for storage as well!
The limit is mostly in materials. You also tend to get space-rated chips made out of ceramic for the packaging, which can also raise or lower the thermal limits.
Anyway, I hope that explains it for you. I can try and answer any other questions, but I'll admit the physics of low-temperature semiconductors is not my forte!
1st Edit:
Here's a link to a wikipedia entry about the idea that at lower temperatures there are fewer electrons which are excited enough to generate a current flow through a semiconductor lattice.
This should give you a good idea of why the resistance becomes higher, and why 0 Kelvin would have never been an option.
You're confusing the operating specifications of the chip with the readout format.
Basically, the Electrical characteristics specify the range of temperatures at which the IC is guaranteed to work properly. This is a physical characteristic of the device. As the datasheet says Operating temperature range, e.g. this is the temperature range over which the IC is supposed to work properly. It has no relation to the theoretical range of the register containing the measurement value.
The temperature sensor readout is specified as "-1 °C/digit". Therefore, each increment of the temperature output equals one degree C. My guess would be that the value of the temperature readout would probably directly correspond to the actual IC die temperature in degrees C, though you should verify this.
The two specifications are unrelated. It's like a car speedometer. My car's speedometer goes up to ~150 miles/hour. However, it's not intended to actually be driven at those speeds. As such, the readout range (0-150 Mph) significantly exceeds the intended operating conditions (~0 - ~85 Mph), as they're different characteristics.
Best Answer
For this kind of IC, the are fabricated on the same process (thus same absolute max ratings and thermal characteristics) and the temperature grade that you buy has to do with the guaranteed test limits on Electrical Characteristics.