There is a little chance of the engines ingesting fluid, which in any case should not jeopardize safety. The risk of ingestion is independent of the depth of the contaminant. Take off is not recommended from an icy runway or runway covered with 2 inch dry snow or 1 inch wet snow. The cross wind limitations for take off and landing for the reported braking action is given in FCOM 2.04.10 page 11
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