Spider-man is legendary within the Marvel universe for his banter, in and out of combat situations. He's the type of person you'd expect to always have something to say, no matter what the situation. Just take a look at this, taken from the House of M story arc:
Iceman is notorious for his sense of humor. Well, his sense of humor, and his lack of maturity. He hasn't been featured nearly as much lately as he was in the past (as a member of the original five, and still a prominent figure in the comic from then on), but every now and again he pops up in X-men titles to throw in a quick joke or two. Throughout the years he's been scolded over his lack of maturity by many different characters; Cyclops and Angel- even Beast, who was known back in the day for his love of alliteration and 'wacky' hijinks- would chew him out from time to time.
It seems fairly official that Iceman uses his sense of humor in order to escape from the hardships he's had to endure- from fighting for his life from the age of 16 onwards, to losing his dad, to seeing his friends die (and then come back to life) around him, to the horrors of genocide, he's experienced some pretty traumatic events. However, Spider-man hasn't exactly lived a charmed life, either. I'm not a regular reader of the series, but from what I know he's endured the loss of his beloved uncle Ben, given up his marriage with Mary-Jane in a demonic pact to save the life of his aunt May, been terrorized by the truly twisted Green Goblin for years, accidentally killed the first woman he ever loved while trying to save her life...the poor guy's seen it all. And while Iceman deals with his issues via his sense of humor, Spider-man actually deals with his problems. He has a job, a love life (he managed to move past the Mary-Jane thing, apparently), and family and friends, all while maintaining his secret identity and fighting crime- usually on his own. Iceman fights in a team, hasn't had a love-life in a long time, has no relationship with what family he still has, and I don't know that he's had a job since he joined the X-men.
So while they could possibly make a strange and awesome team, Spider-man and Iceman are very, very different.