It sounds like you may have a couple issues going on. Gurgling noise from drains is often due to a clogged vent pipe for the plumbing. You need air flow behind flowing drain water for proper draining so if the vent pipes get clogged from debris, bird/critter nests, snow/ ice buildup, etc.., it can slow down the flow of drain water which creates clogs or a suction in the system and gurgling drains. I'd say check the system vent pipes on the roof if possible. A plumber can use a borescope if needed to check for clogs in the system.I use a trick where I insert a short piece of flexible garden hose into the toilet drain hole in the bottom of the bowl...just enough to reach up into the toilet where it curves into an S which allows air into the drain system. Or remove a P trap from one of the nearby sinks temporarily. Then try flushing as usual or pour water down the toilet or another sink and see if the gurgling noises do not occur. If so, that shows that you need more airflow in the vents.
Another issue may be how the drain field is setup. Do you have an outside pit which stores water/sewage until it's pumped into the field? If so, then you may have a problem with the float in the pit or the pump is not working to eject effluent to the field....blown breaker,bad pump, wiring damage, etc..Most systems like that have a warning device/alarm in the house or garage which beeps if the water level in the drain pit gets too high but that alarm may be not working, etc.. Check to make sure that pit is not too full and working properly or causing a backup in the system. Check for any blockages in the drain pipes/ lines to the field...frozen pipes, etc.. My brother had one situation where a guy dug trenches to run electric power to a shed and nicked the drain pipe just enough for sandy soil to get in and clog it up.
If the bathtub drain.trap is frozen, then you will need to get under the bathtub area /crawlspace and defrost the pipes with a space heater or hair dryer...then insulate the pipes or wrap them with heat tape and use that when temps get too cold. You can try pouring rubbing alcohol down the tub drain which will also thaw/deice the trap but may still need to insulate the pipes/trap at some point.
Home centers or plumbing suppliers, etc.. also sell caps or plugs to cover an unused toilet drain pipe/flanges...might be a better, water tight solution than a temporary cover or seal.
https://www.google.com/search?rlz=1C1AOHY_enUS709US709&ei=9PZMWtK0HumMjwSJ3pKQBA&q=toilet+flange+cap+&oq=toilet+flange+cap+&gs_l=psy-ab.3..0l2j0i22i30k1l7.3537.8903.0.9092.29.20.0.3.3.0.142.1702.8j9.17.0....0...1c.1.64.psy-ab..11.17.1389...46j0i67k1j0i131k1j0i46k1j0i131i67k1.0.AY20J_q3gp4