I would think that you'd end up baking the item, not smoking it. You need to get enough heat to the wood chips to get them to smoulder, without directly heating the item to be smoked.
All of the times I've seen people on cooking shows attempt to rig up a smoker like you descibe, they've done it stove top, not in the oven, and it tended to be in a pan a little heavier duty than a disposable aluminum tray -- it looked more like a deep hotel pan to me, and I don't think they vented it 'til they were done.
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That being said, I still occassionally grill outside in the winter. Okay, I admit, it's usually because the power's out, but I did it last weekend as a favor to my neighbor so he could serve steaks to his wife and mother-in-law for the day before Valentine's day ... in that case, it was actually fairly warm (maybe 45-50°F), but I've also done it when we've been buried in snow and ice.
The important thing about winter grilling is to keep the lid down, and not check on things too often. For long and slow cooking (I think I was trying to finish a stew), I've rigged up things to insulate the grill ... although, I managed to cook one of my leather welding aprons last year.
But for cold smoking ... you're all set ... you can get get insulation blankets for your smoker, and then you just need to keep the fire going in the hot box.
From what I can tell you're generally on the right track here. From what you've said, there are probably just a few issues.
tough/dry/rough. Believe it or not not cooking long enough could be the problem here. You want your brisket to get in that 190-200 range, this will cause the connective tissue to break down and make it very nice. The other possibility here (and you didn't say so we don't know), is that brisket can be very tough if it's not cut properly. You need to cut the flat across the grain for it to be tender as it's a very long muscle.
Lack of a smoke ring. This is what we call the pink ring around the outer bit of the meat. You don't want the inside to be pink, you want the outside to have a pink ring around it. This can be unpredictable in formation and depends on a lot of things. If you liked how much smoke flavor your meat had, I wouldn't change anything, but if you wanted more smoke, try to either put in more wood chips at the start, or put them in dry (careful though, you don't want them to burn, but wetting them really just slows the burn time). From what I've read, the smoke ring forms early, so the first hour or so is the important part here.
Foil. This is hotly debated in the BBQ world. I only foil if I need to hold my meat for a period of time (if I mistime and finish early I'll wrap it up, drop it in a foam cooler with towls), but a lot of people swear by it for producing juicier meat. Totally up to you, experiment here.
Lastly, a few bits of advice (I've done a couple of briskets now, all on charcoal though). Don't bother to sear the meat, let your smoker take care of the whole cook. Do that, make sure you get your meat up to temp (brisket is hard to tell without a thermometer as it doesn't have a bone you can check, so go get an instant read one, they aren't too expensive). As far as the dry rub goes, that's a matter of taste, a lot of folks put it on the night before, but the meat gets plenty of flavor just applying it right before you put it on.
Best Answer
Convenience: It's more convenient and easier to monitor the temperature inside the home. The oven has a thermostat, where the grill temperature needs to be monitored and adjusted manually.
No smoke left: Is could be assumed that the smoke has been exhausted.
Too much smoke: The smoke flavor could become too strong if finished on the grill.