Spacesuit designers and extravehicular activity (EVA) planners would probably prefer if spacewalks only took part in the Earth's shadow. From the spacesuit design perspective, one of the biggest issues is heat rejection, not heat retention. This is because of nearly nonexistent convective heat transfer (conduction and advection) in near vacuum in LEO so the only way to keep suit internal environment's temperature at acceptable levels is by either radiating, rejecting or storing it. Large (and massive) radiators on mobility units obviously wouldn't be very welcome, so while some smaller heat sinks and heat exchanging radiators are used internally in the PLSS (Portable Life Support System) units, we're only really left with heat rejection and excess heat storage options.
Rejection of external environmental heat is pretty straightforward. Spacesuits are mostly white or use reflective surfaces to prevent absorption and reflect as much of incident light from the Sun and Earthshine (Earth's albedo) before it's converted to photothermal, or if you want, photoexcitation heat. This also helps prevent photoelectric charging of suit's outer layers, which could also be dangerous if too much charge built up and would be rapidly (sometimes referred to as catastrophically) discharged upon touching the station's truss, for example.
Suit internal thermal environment is a bit more tricky. Design parameters on average work with 1,200 BTU (British Thermal Units) per hour, about 350 W if memory serves correctly, of so-called metabolic rate. In simpler terms, this is design ceiling heat output per hour during an active spacewalk. All this heat, with spacewalks sometimes lasting even over 8 hours (current Russian spacesuits can support longer spacewalks than American, but are more clumsy with umbilicals - i.e. they're less autonomous) has to thus be transferred to cooling water and rejected using the sublimator in the PLSS http://quest.nasa.gov/space/teachers/suited/5emu4.html One limit to EVA time is the amount of water remaining. As mentioned, Russian spacesuits (Orlan) can extend their autonomy with the use of umbilical connections to the station, while American (Enhanced EMU w/ SAFER) can last 8 hours plus 30 minutes of backup (redundant life support), having about 820 Wh of total power available to them.
So when EVA is taking place in the Earth's shadow, despite spacewalkers having to switch on a few lights mounted on their helmets, PLSS active heat rejection system has to work less with no external, incident heat sources and their overall power consumption is during those times lower. So from suit design perspective, being in the Earth's shadow is an advantage.
From EVA planner's perspective, it's a bit of a mixed bag. In Earth's shadow, there's no worry of increased solar flux (solar storms and other events), but it might be a bit more difficult for astronauts to retreat back to the airlock in case of an emergency, and they might work a bit slower too due to reduced visibility. So if all the duration of an EVA took place in the shadow, it would be an advantage, but as transits in and out of them take from EVA time (astronauts would be adjusting their PLSS for thermals, work more with their suit controls like switching lights on and off, adjusting cameras,...), it's not really an advantage.
As for astronauts themselves, they would probably prefer all EVA take place during daylight. They don't have to take so much care about external fluid leaks (such as ammonia from the station's cooling system) since they'd bake-off (outgas) faster on the sunny side. They also see what they're doing much better, can work faster and perhaps even progress to tasks otherwise scheduled for next EVAs, and the view is much nicer too. This is when they'd take their cameras out and take a few EVA portrait shots, selfies or whatever is now trending. Having watched quite some spacewalks (including recent Wilmore & Virts ones), I'd say they also become more chatty and generally the working atmosphere (pardon the pun) seems more uplifting (there I go again, sorry). :)
The Enhanced EMU Suit (with lights on). The suits are white to reflect heat and to stand out against the blackness of space; the red
stripes serve to differentiate astronauts. (Source: Wikipedia, Credit: NASA)
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