How long should it take for the adhesive to dry in colder weather?
Cold weather can indeed severely retard the curing time of the adhesive, as can the temperature of the substrate you are tiling onto. This is due to the fact that modern adhesives cure by a chemical reaction therefore the colder the temperatures, the slower the reaction.
It is therefore recommended that a blow heater be placed in the room prior to tiling to increase the ambient air temperature and that of the substrate should it be a necessity to tile in cold conditions.
Cleaning the backs of the tiles of any dust or cutting residue is recommended to ensure a good bond between the tile and the adhesive but I am a little concerned as to why the adhesive has stuck to the floor but not the tile. This would suggest that the acrylic bonding agent was not used to seal the sub floor prior to tiling, can you confirm whether or not this product was used and if so, onto what type of substrate and in what dilution the product was used? The acrylic bonding and priming agent is a product that promotes adhesion and reduces the porosity of a variety of surfaces and is considered to be an integral product in the installation of natural stone tiles.
It should not be necessary to butter the backs of the Brazilian slate tiles as they are very consistently riven and with the recommended 6mm notched bed of adhesive, there will be more than enough coverage over the back of the tiles. It would also not be necessary for the tiles to be completely dry before installation begins.