I design septic systems in Texas. Several thoughts -
1. If your lateral pipes are filled with frozen water, the gravel in the drainfield must be full and frozen as well. If the drainfield is frozen, you will still have problems.
2. Could you just rent a heated pressure washer to blow hot water into the pipes to defrost the laterals and the drainfield?
3. If this is going to be an ongoing problem, consider replacing your gravel and pipe drainfield with a drainfield that uses Infiltrator panels (if your state allows them). Look them up on the web.
