It's not an entirely reasonable assumption that the whole planet is like the people near the gate, but it's not an entirely unreasonable one, either.
Generally speaking, considering Stargates can be relocated rather easily at least for advanced technologies, they're placed at a location where they'd be useful.
So, if you found a Stargate in a glacier, it's a somewhat reasonable assumption that that's what the whole planet is like... otherwise, why not move it to a better location? I believe Carter only declared it an ice planet once she got to the surface and saw there was nothing but snow and ice as far as the eye can see, which means she's probably at least more open to thinking otherwise before that, like maybe there could have been an arctic-based civilization. In any event "ice planet" is, for their purposes while they're stranded and in need of help, pretty much the same as "completely ice-bound location on a planet with no signs of civilization".
When there are humans involved, usually they're brought there by the Goa'uld, and it's usually for some purpose. In such situations, they would both keep the culture more or less consistent (some may want to be worshiped in the Greek style*, or the Egyptian style, but generally they're not the type to say "hey, you worship me as you'd like" since that tends to open the door to "what if we DON'T worship you then?"), and probably keep them relatively close to the gate, as well... if your main purpose is mining, what use is having loads of people far from the mines who might want to launch an uprising? If you're breeding soldiers, you might want a higher population, but you'd still want them to be able to get to the Stargate if you're launching a ground assault through them.
And while there's a whole planet out of range of the Stargate... it's usually also out of the range of being of immediate interest to the SGC. I mean, a planet may have great farmland and a thriving culture on another continent, but if everywhere near the Stargate is frozen tundra and a small hunter-gatherer tribe, then they're likely not to find that other culture until they do a detailed survey, so that farmland isn't much use to them nor are they likely to make use of anybody but the hunter-gatherers as trading partners. When writing up their reports, they're probably going to focus more on the immediate gains, and so that'll tend them to describe the planets a little more reductively.
Of course, there are sometimes cases where there are multiple different cultures, like Jonas' people, or the ones who had a religious war over the Stargate, and in such cases thinking so simplistically can come back to haunt them.
(Atlantis has a similar excuse in that most of the planets are culled to small populations by the Wraith, and so they can't really build up a set of diverse cultures on any one planet.)
*- Not a euphemism.