* C$ flat versus greenback, pares earlier gains * Canada starts vaccinations, with frontline workers inoculated * Canadian bond yields mixed; 10-year up slightly (Adds new comment, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Dec 14 (Reuters) - The Canadian dollar was little changed to slightly higher against the U.S. currency in thin trading on Monday, as optimism about a Brexit trade deal and progress in the global rollout of COVID-19 vaccines was tempered by stricter lockdowns in Europe. Germany, Britain, and the Netherlands on Monday announced tighter restrictions going into the holiday season. So far this month, the Canadian currency has gained about 2%against its U.S. counterpart. "We have a pretty positive outlook on the Canadian dollar," said Erik Nelson, currency strategist, at Wells Fargo in New York. "The policy mix in Canada is positive. Yes, the BoC (Bank of Canada) is leaning toward easing, but so is every other central bank. If anything, the BoC has slowed its balance sheet growth and fiscal policy is still going full steam ahead. So I think that"s a pretty positive mix," he added. The BoC said last week it could lower already record low interest rates if a second COVID-19 wave leads to more scarring, Deputy Governor Paul Beaudry said. Market risk-taking got a boost earlier after European Union Brexit negotiator Michel Barnier said on Monday a trade agreement with Britain was still possible before the country"s final break with the 27-nation bloc on Dec. 31. In afternoon trading, the Canadian dollar was flat to modestly higher on the day at C$1.2762 per U.S. dollar . Since late October, the Canadian dollar has risen 5%. Also helping the Canadian currency was news that Canada kicked off its inoculation campaign against COVID-19 on Monday by injecting frontline healthcare workers and elderly nursing home residents, becoming just the third nation in the world to administer the Pfizer/BioNTech vaccine. U.S. crude futures, which have more or less a positive correlation with the Canadian dollar, rose 0.9%% to $46.99 per barrel. In the bond market, Canadian government bond yields were mixed, with the Canadian 10-year yield slightly up at 0.718% , from 0.716% late on Friday. (Reporting by Gertrude Chavez-Dreyfuss, Editing by William Maclean and Richard Chang)