1) Ride a bike yourself. Not to work, obviously, but every weekend, get your butt on a bike and GO, bringing her along with you. It's easier to do things for the first time when there's someone else along, and she'll become more familiar with the route and such.
2) ...seriously, being scared of people because they are LOWER INCOME doesn't sound accurate. Has she been catcalled or harassed or something? Are there no streetlights, broken streetlights, streets covered in broken glass? If so, find a route that doesn't involve the area in question, and remind her that she's a lot faster on a bike than people can run.
3) Or does she not feel safe riding her bike on streets? If so: again, you'll have to break the ice on that one.
4) Better safety gear may help: bright headlight/taillight, for starters, snow tires in the winter.
Seriously, my husband and I bike everywhere, in Chicago, year-round. With a four-year-old, even. Unless y'all are on a freeway or in an area prone to drive-by shootings, I am unimpressed.
(And Argyle, ya wuss: this year we're supposed to have a mild winter. 2013 was insane, but the two years before that were a big nothing, and last winter was balmy by 2013 standards.)