Do traditional bonsai pots have greater tolerance to cold and ice thereby making them less likely to crack??
Absolutely! Real bonsai pots are made from a much better quality clay than terracotta. Especially when you go for the somewhat more expensive pots like Tokoname. Also take care to place deciduous trees in a glazed pot and conifers in a non-glazed one. This is better for the tree as well as the pot.
I have really nice loamy garden soil so I think that just gently sinking the whole plant to the soil level and mulching in a little with straw should save them from shock and death.
This gives my a very good clue on why your pots tend to break and your trees are less hardy. The soil you are using is just too compact and holds too much water. This is fine for garden plants which are generally less valuable but totally not suitable for bonsai. Because this soil is so compact and holds so much water, there is no room for the water to expand when it starts to freeze so eventually the roots get crushed and the pot breaks. For this reason we generally use a more grainy and porous mixture of akadama and kiryu for our bonsai or kanuma for azaleas. Sometimes cat litter can be used as a cheaper alternative, but it also requires more cleaning work before it can be used as bonsai soil.
I really advise you to spend the effort of transplanting your bonsai into a mixture which is better suitable for bonsai. For conifers you could already transplant them into a mixture of 1/2 akadama and 1/2 kiryu now and give them a better chance of surviving the winter. For deciduous trees, I would wait until spring to transplant them into a mixture of 2/3 akadama and 1/3 kiryu. You must protect the deciduous trees in a shed and you can leave them there al winter. Deciduous trees don't need any sun-light while they're dormant (No leaves).