What's the most efficient riding style for losing weight? I plan on setting up my bicycle with one of those devices that holds the rear tire and gives some resistance so I can exercise through the winter.  I think it's called a bicycle trainer.

When using one of those for weight loss: Is it better to ride for a long time on low resistance or at a low speed?  Or is it better to ride harder, spinning your legs faster or with more resistance for a shorter amount of time?

Sorry; there isn't even an exercise tag on here.  Feel free to retag as appropriate.
The answer to this question is dependent on a number of factors, but the short answer is just 'yes'. 

If you are purely looking for weight loss then the equation is calores in minus calories out equals delta, and so long as the delta is negative, i.e. that you burn more than you consume, then you will lose weight. It's just simple arithmetic. 

So, in the first place, just eat the same as you have ever done and do more exercise, then the weight will come off. 

To do more training, though, will also require a balanced diet. If you up your training load without changing your diet, you will get more tired and notice other negative effects. You'll be hungrier, you'll eat more, it's not as easy as just upping the workload.

What you're actually asking is about making this weight loss more efficient, maybe even drastic, and getting the bang for your buck. So if you sprint, on a higher resistance, with higher cadence, then your heart rate will be higher and you'll burn more - but you'll be able to maintain it for less time. But if you try for a low cadence, with low stress, you'll maintain for a lot longer, but you'll burn less quickly. You'll lose weight either way, but you'll also do it differently and prepare your body differently. 

To do this properly, you'll probably want to work just below the anaerobic threshold, this is the point at which the body is still able to consume enough oxygen to assist the work through using sustainable sources within the body (i.e. fat stores), but without all that pesky lactic acid being produced (and burning other sources, e.g. muscle). This is the point where many endurance athletes will try and aim their training (also known as LSD - Long, Slow, Distance), to sit for extended periods at a heart rate set at a maintainable point. You'll need a heart rate monitor and a means to test yourself. For a reasonably trained athlete, this will likely be around 150 bpm. 

For what it's worth, my rule of thumb is that I'll burn about 40 calories per mile almost irrespective of speed ... but if you really want to lose weight, go running. I reckon I burn about 120 calories a mile when running.