Absolutely fine. Max safe charging current goes to so close to zero that it's a very good idea not to try charging at all; also because manufacturers often specify max charge current as a simple step function forbidding it completely below 0degC or -5degC. (If you engage in a big project with the cell manufacturer with NDA and stuff, then they would come with actual curve sets on allowable charge currents, which would be non-zero even at very cold temperatures.)
Discharging is fine; DC ESR skyrockets, but that isn't a problem for a 10mA load. Larger loads cause more self-heating which in itself isn't dangerous but to be on the safe side you might want to avoid doing that; maybe too quick heating could cause mechanical issues within cells. Hotspots and uneven thermal expansion, the usual stuff. But 10mA definitely isn't a problem. If it were my project, I would consider limiting myself to 500mA or so, also for efficiency and ability to fully discharge; if I need more current than that, then parallel more cells. You see, in cold the terminal voltage sags more and last thing you want is having to stop because of reaching cut-off limit already at 50%SoC.
Same and similar cells are used below the -20degC datasheet ratings; but li-ion batteries being specialty components, each customer gets their own datasheet. It's only us small players who need to work with generic datasheets (usually with pretty limited information).
For an interesting reference, I drove my Nissan Leaf, which does not have battery heating*, which had sat outdoors at between -25..-30 for a few days; the BMS limited discharge power from the usual 160kW (2.6C for the 62kWh pack) to 70kW or something (1.1C). Take this with a grain of salt, but this gives you a rough idea how manufacturers who give long warranties on their batteries treat their cells in extreme conditions.
*) the smaller 40kWh version does have a small pack heater