I do both. For lagers, I'll bottle them. Yes, carbonation does take longer when it is cold.
When I do a lager, I'll ferment around 45 or so like I said before until it is about 80% complete, as measured by a hydrometer. Then, I'll remove from the fridge and allow to warm to room temp for about 3-4 days for a diacetyl rest. Check gravity again to ensure it is done. When complete, rack and cool down to about 33 or so a degree or 2/day. Keep at that temp as long as you can. This is your lagering phase. After this, warm up to room temp and package.