"Juddering" is as good a description as any of how a diesel runs when not all cylinders are firing. Gray smoke from the exhaust is unburned fuel (i.e., it has been injected into a cylinder, mixed with air, but not burnt).
If your Golf is new enough to have a catalyst (many VW diesels are), then unburned fuel in the exhaust will quickly damage it, so you want to fix this. However, it's much too early to give up on the engine! Most likely, one or more of your glow plugs have failed (so they don't heat up the cylinders and promote ignition when the engine is cold), or the system that turns them on at cold start is malfunctioning. I can't give more details without knowing how old the car is--on older diesels ('80s VWs and Mercedes, for instance) there is a simple relay that can easily be tested, while on newer ones (VW TDIs, for instance) the glow cycle is computer-controlled.
EDIT: If you can rule out the glow plugs, there are a number of other less likely possibilities. Anything that restricts fuel or air flow on a diesel engine can cause incomplete combustion (and hence, again, gray smoke). This would include clogged fuel or air filters, for instance. The fact that your car is a 2000, though, makes me think of one particular common problem with VW TDI engines from 1999-2003 or so: soot buildup in the EGR system. Fixing this requires removing the EGR valve and intake manifold and soaking them in solvent to clean out the soot. It is a simple job but time-consuming (and therefore expensive if you have to pay someone else to do it, unfortunately).