Farming in the mid-latitudes in winter is a tough prospect under the best of conditions. Heat isn't the only problem, though it's a tough enough problem to solve. The quality of light in mid-winter just isn't high enough to make most types of food production worth the effort. You can sprout seeds, because they don't need light. However, once the starch in the seed runs out, the plant has to have enough light to grow. New York in the winter just doesn't have enough light for long enough in the day for most food purposes.
This isn't to say that you couldn't do something worthwhile with enough planning and the right crop mix. However, arriving in mid-winter without the appropriate facilities, etc. in place is not a promising start to the effort. Even winter wheat doesn't really grow during the winter--it survives in hibernation. A force of 5000-6000 probably will need to requisition supplies from the locals.
Using a bicycle to heat a planting box to grow crops is probably represents a net energy loss. A windmill or a water wheel might be a better bet.
Greenhouses can extend the growing season significantly. This is especially true in locations where the late-season temperature is more of an issue than the quality of light. In southern New Hampshire, for instance, the growing season is in excess of 120 days, which is long enough for most crops. In Berlin, NH the growing season is less than 90 days. Greenhouses enable real-world gardeners to start their seeds early and, if the plants are kept indoors, harvest them later than would be possible outdoors. The best option for subsistence farming in marginal areas like Berlin, NH might be to start the seeds early, then get the sprouts into the ground right after the last killing frost occurs. The locals still would need a lot of greenhouses to start seedlings for the acreage to support 10,000 people, but the space demand for starting seedlings is a fraction of what would be necessary to keep the plants indoors past the first killing frost at the end of the season. Greenhouses don't grow on trees, so some sort of compromise between growing practices and infarstructure will have to be made.
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