First of all, let me preface my remarks by pointing out what should be obvious: Tents are not insulated. So any comments about one tent being "warm" and another not is purely relative.
But clearly, double-wall tents are warmer in the winter (and cooler in the summer), for exactly the reason your friends mention. The air space between the fly canopy (the inner part of the tent) and the fly can indeedin still or light-wind conditionscreate an insulating layer of warm(ish) air. Under the right conditions such a tent can even be downright balmy. With a single-wall tent, all that stands between you and the cold, cruel world is that one thin layer of fabric. During the summer, a double-wall tent also can be a little more comfortable because the fly literally shades the canopy, although most tents still become ovens in the sun.
You have to weigh that against the weight savings of a single-wall. Sierra Designs' new four-season Pampero ($359; www.sierradesigns.com) comes in at about six pounds, 11 ounces for everyday use, which isn't bad (it can be stripped down to less for mild weather). Your Omega is slightly heavier. Bibler's very tough, very minimalist I-Tent ($539; www.bdel.com) goes for four pounds, five ounces. So that's fairly significant, although the I-Tent lacks a vestibule, which can be a handy thing in severe weather.
In any event, that's a lot of dough to save basically two pounds. I'm inclined to say you're perfectly well off now. Camp on!
For a bevy of tents to settle any debate, check out Outside Online's Tents Buying Guide.