A snowy video indicates that your input signal is relatively weak. On the other hand, a noisy picture is when there are too much interference is super imposing on the video.
Snowy picture comes about when the signal coming in the RF INput (Ant/Cable) at the back of the unit is below a certain level. If this is the case, then it is not a problem with your TV but rather your aerial (antenna) or the cable from your provider. A way to verify that it is the ant/cable that is the cause and not a defective TV/tuner is to hook up an old VCR set to Ch. 3 or 4 to the RF IN of your TV using a short 75 ohms coaxial cable terminated at both ends with FP-5 connector. Play a known clear good tape and set your TV to Ch. 3 or 4 as the case maybe. If the picture is relatively clearer, better, then you have just confirmed that it is indeed your aerial or your cable (provider) that needs looking into. If on the other hand, the VCR signal is also snowy then chances are that you have a problem with the input stage of your TV including possibly your tuner.
For your aerial problem, antenna orientation or replacing with a higher gain antenna might help solve the snowy signal. For your cable problem, you have to call-in for service from your cable provider. If it is a TV problem, your best course would be to seek the services of a qualified TV technician since this involve electronic circuitry analysis, diagnosis and possible component replacements.
Additionally, you may try looking for any loose connection, loose grounding, broken wire or anything out of the ordinary in your connections.
Hope that this be of some help/idea. Pls post back how things turned out or should you need additional information.
Good luck and kind regards.