On certain scenes, the video picture becomes extremely low-quality, blurry, and pixelated--even if the encoding bit rate is set very high (7.0+). Then after a minute or two, the quality snaps back to normal.
I've seen this happen on other DVD recorders and capture cards when the device was overheating; specifically the capture chipset. How often do you run this unit, and how long has it been in service? It could be one of several things:
(1) The heatsink on the mainboard encoder chipset needs to be re-seated, because the old thermal grease/tape has turned to powder.
(2) The heatsink never had grease/tape, and some environmental change cause a slight shift that no longer makes perfect contact. Not having grease/tape is a lousy design, but it happens.
(3) There is no heatsink on the capture chipset, and it simply overheats more and more as time goes by, meaning it's been damaging itself for years with heat abuse. This is also very common, the result of cheapness (and stupidity) on the part of device manufacturers. This is why so many devices are "throwaway now", and this is how a device can have an expected shelf life (after so many hours of use, a component will simply give).
I don't believe this has anything to do with the hard drive.
There's actually a whole list of possible issues, from blown caps and fuses inside the unit, to under voltage by the power supply, to the suspected hard drive. But what you describe is a processing error -- not data rate (hard drive), not power related (unless it's specific power to the chipset that caused it to semi-hibernate).
Snow should actually increase processing, not reduce it, because it's near-pure noise. So if that was indeed a triggering factor, that points more to a processing error (and potentially a power-related error, to the processor).
I know we have these conversations in private a lot -- fixing equipment sucks. For somebody like you and me, it's even more damning, because we know how to fix the easy things. It's these complex problems that can waste so much time. And that's not even counting time required to find an answer.
I have already unplugged and replugged it
You REALLY need to be careful with this.
I'm sure you know this already, but it's worth the mention to anybody else that does not. Unplugging a lot of modern electronics, even when turned "off", can be as bad as unplugging it while it's turned on. These devices are never truly "off", and are often referred to as "energy vampires" for that reason. The Toshiba is a more serious offender, because the fans are always running, and the unit is always processing for TV programming guide updates -- even if you don't use it for TV recording. When you yank the plug, you always take the risk that the capacitors or other circuits will fry out, the same as an electrical surge. Because when you really get down to it, that's what you're doing -- manually creating electrical surges! I know, it seems insane, but that's what's happening. I have a damaged Panasonic AG-1980 because of this, and I damaged a Panasonic DMR-ES10 recorder years ago for the same reason. I also believe my dead JVC HR-S3800 was a victim of unplugging/re-plugging.
Excellent quality recorder, these Toshiba XS35 HDD units, but not without their imperfections.
The fan is the only reason I passed on those recorders. It always seemed like a fire hazard to have a component run 24/7/365, whether I wanted it to or not. And then the only way to force it off was to kill power entirely, meaning risk of damage at each use.