Both sides lost several ships to weather during the war, as well as many more suffering damage during storms. However, the losses had comparatively little effect on operations - the lost ships were destroyers, with most navies having sufficient of these to make up for the losses.

A total of eight destroyers were lost to weather during the war; one French, one Soviet, two Italian and four American. The losses are given in the following table:

The French Branlebas broke in half in a moderate gale (7 on the Beaufort Scale). She split at the break of the forecastle (where the forecastle meets the main deck). This was a relatively sharp break, which tended to concentrate stresses, and cause cracking of the plates at this point. This combined with the French Navy's acceptance of higher stresses in their destroyers to cause her loss, though investigation of her sister ships also showed that she had poor stability. The two Italian destroyers were lost while returning from the 2nd Battle of Sirte, in the same storm. Lanciere was lost after waves crashing over her superstructure caused flooding from weak hatches and doors, which in turn disabled her engines, leaving her unprotected from the storm and ultimately resulting in her capsize. The cause of Scirocco's loss was likely similar. For Sokrushitelnyi, a wave broke over her stern, again causing flooding through weak hatches, and disabling her. Warrington was sunk by the so-called Great Atlantic Hurricane of 1944. Strong waves breaking over her and a heavy roll allowed water to flow down her intakes, and again causing her to lose power, ultimately causing her to capsize. The three American destroyers lost on the 18th December 1944 were lost in the Pacific, during Typhoon Cobra. Admiral Halsey had taken Task Force 38 into the storm, following poor interpretation of weather reports. The destroyers had been low on fuel, and failed to take on ballast in preparation for the storm. The wind caused the ships to heel over, allowing water to flood through the boiler intakes, shorting out the electrical systems, and causing the ships to then lose control, and allowing the weather to capsize them. Many other ships were damaged by this storm. Aboard the carrier Monterey, aircraft broke lose in her hangar, starting a major fire, while many other carriers suffered to a lesser extent from a similar problem.

Three navies did not lose major vessels to weather during the war. The Royal Navy had established a relatively stable hull-form for its destroyers, which it used throughout the war. The design section were worried about the dangers of capsize, and took steps to protect ships against it. Topweight was reduced, and older ships told to take on ballast below a certain fuel level. British stability criteria were generally stricter than those in place in other navies, though they would not have protected against the vagaries of Typhoon Cobra. However, they did lose the cruiser Effingham after she rammed a rock in a Norwegian fjord. The Imperial Japanese Navy had experienced a number of ships lost or heavily damaged to weather before the war. the Tomozuro to weather in 1934. They also suffered heavy damage to two destroyers, the Yugiri and Hatsuyuki the following year. Both ships lost their bows, which can be seen in this image of Yugiri. The damage was sustained during exercises carried out by the Japanese Fourth Fleet, which suffered damage to several other ships - the cruisers Mogami, Myoko and Mikuma all took some flooding, the submarine tender Taigei developed serious cracks in her hull, and the welded hull of the minelayer Itsukushima was severely buckled. This incident (known as the 'Fourth Fleet Incident') and the loss of the Tomozuro led to major redesigns of Japanese ships. Top weight was reduced, greatly increasing stability. For example, the Chidori class destroyers had their 5-inch guns replaced with lighter 4.7-inch weapons. Ships had extra ballast, keels and bulges fitted to increase stability. Welds were replaced with rivets wherever possible, and where it was not, extra plates were fitted. The Kriegsmarine, meanwhile, mostly avoided loss through the simple expedient of spending very little time at sea. A number of their destroyers had very poor stability, to the point where special ballast had to be fitted to avoid sinkings. They also avoided exposing their destroyers to weather when necessary - in the run-up to the Battle of North Cape, Erich Bey ordered his destroyers to withdraw to avoid weather damage, leaving Scharnhorst unprotected against British destroyers.

Weather damage was far more significant to naval operations. The North Atlantic convoy routes provide a clear example of this. D K Brown gives a table listing the percentage of escorts unavailable for operations during the war:

It should be clear that, on average, the worse winter weather resulted in more escorts being unavailable for action. However, this was not a universal trend, as many other things could remove a ship from operations - battle damage, maintenance tasks or refits. Weather damage was a near constant trend. Waves tended to damage the superstructure, crushing bridges and funnels. Aboard one old S-class destroyer, her captain was killed in his bunk by a wave breaking over her bridge and destroying his sea cabin. Fittings like boats were frequently swept overboard. Wind and wave could cause collisions between ships, or break up formations. Finally, crews, particularly in exposed positions, could be swept overboard. Weather also had a more insidious effect on crews. Constant rolling and slamming (up and down motion) exhausted crews, and could cause sea-sickness. Similarly, being wet was not good for the health and morale of crews, especially since, on many ships, water tended to leak into the mess decks.

Sources:

• Fourth Fleet Incidents - Japan Has to Revamp Her Navy – 1934-1935, Anthony Tully, Bob Hackett and Sander Kingsepp, combinedfleet.com, 2012, http://www.combinedfleet.com/Fourth-Fleet-Incident.htm

• Nelson to Vanguard: Warship design and development 1923-1945, D. K. Brown, Seaforth, 2012

• Atlantic Escorts : Ships, Weapons and Tactics in World War II, David K Brown, Seaforth, 2007

Yes on a few occasions.

The most notable one coming in December of 1944 off the Philippines when the US 3rd Fleet was hit by a Typhoon. The fast carrier force had completed air strikes on targets ashore in support of landings, and was in need of refueling for many ships, and due to Halsey's questionable choices, and a degree of bad luck the focal point of American naval power sailed right into the storm.

800 men died and 3 destroyers sank, with many more damaged and requiring extensive repairs.

I write more about it here, along with a few other notable storms the USN dealt with in the later years of the Pacific War. https://www.reddit.com/r/AskHistorians/comments/70a8u4/was_there_any_hurricanes_during_the_pacific/

Absolutely.

The most significant storm was Typhoon Cobra. On December 17th Task Force 38, which included 70+ ships including 13 carriers and 8 battleships was sitting to the east of the Philippines. They had been conducting air raids against Japanese airfields in the Philippines. Low on fuel and other supplies they had pulled back to refuel and rearm, when the storm came up on them. Misreading the size, strength, and position of the storm Admiral Halsey directed the fleet to sail directly into the center of the storm. For two days the fleet was battered by the storm.

The damage was significant. Just under 800 lives were lost. Three destroyers were sunk (USS Spence, Hull, and Monaghan). At least 100 planes were damaged beyond repair. On three carriers major fires broke out as the seas were rough enough to knock planes around on their decks. Virtually every ship sustained some damage, and a number of ships sustained enough damage to need to be pulled from the theater to conduct repairs. For example USS Monterey spent six months in Bremerton Washington being repaired. USS Iowa had to go to San Francisco to repair a broken propeller shaft. Most damaged ships though were only out for a month or two being repaired at the forward Naval Station at Ulithi.

Admiral Nimitz later said, “[it] represented a more crippling blow to the Third Fleet than it might be expected to suffer in anything less than a major action.” Ultimately the storm didn’t significantly delay operations in the Pacific. The Japanese Fleet had already been battered into near irrelevance, operations in the Philippines were well underway and most ships were back in service in time for Iwo Jima and Okinawa in the spring. So the temporary sidelining of a significant portion of the Navy’s combat strength didn’t really slow operations.