No the weather radar won't help you (much). Obviously you can use the radar to avoid flying through precipitation.
Otherwise you have to use common sense:
E.g. look out the window. Even at night you will see when you are flying in clouds. As well you can keep an eye on outside air temperature. Engine anti-ice is still available, and the wings are not going to accumulate ice at e.g. -30 deg C.
Risk of wing icing is predominantly from -10 deg to a few + deg C. And high moisture contents, which can be seen early on as small droplets forming under the wipers.
A way to deal with it is not to stay in the layer with those temperatures for too long, like descending faster through it, to minimise exposure. Another way is simply to increase speed which will will increase the total air temperature.