* Jobless claims fall 3,000 in February payrolls survey week * Consumer prices up a bit in January, heating costs jump * Mid-Atlantic factory activity falls sharply in February By Lucia Mutikani WASHINGTON, Feb 20 (Reuters) - The number of Americans filing new claims for unemployment benefits fell last week, suggesting the labor market continues to steadily improve despite severe weather that could hold back hiring again this month. Cold temperatures continue to inflict pain on the economy, with other reports on Thursday showing a surprise drop in factory activity in the mid-Atlantic region this month and a spike in electricity and heating fuel prices in January. "This has been a terrible winter. Weather has definitely been a factor in keeping things slow," said Alan MacEachin, an economist at Navy Federal Credit Union in Vienna, Virginia. "Looking at everything right now, I don't know how we can get a good picture for probably at least a couple of months." Initial claims for state unemployment benefits slipped 3,000 to a seasonally adjusted 336,000, the Labor Department said. The claims data covered the period for February's nonfarm payrolls count. Snow storms slammed parts of the country last week, which could have kept some workers at home, and possibly held back payrolls growth in February. "This would suggest a deleterious impact on February's payroll numbers," said Guy Berger, an economist at RBS in Stamford, Connecticut. Bitterly cold weather was blamed for a sharp slowdown in hiring in December and January's marginal bounce back. But claims have been tucked in a 325,000-348,000 range this year, suggesting no fundamental shift in labor market conditions. The severe weather also took its toll this month on manufacturing in the mid-Atlantic region. The Philadelphia Federal Reserve Bank said its business activity index tumbled to -6.3 in February, the lowest in a year, from 9.4 last month. Economists had expected the gauge of factory activity in eastern Pennsylvania, southern New Jersey and Delaware to come in at 8.0. The region has been blanketed by snow storms. A reading below zero indicates a contraction in manufacturing. A gauge of factory employment in the region slowed sharply, while orders hit a nine-month low. Some of the pull-back in activity is likely related to firms selling off inventories after a huge stock build-up in the second half of 2013. "We suspect that a large portion of the weakness can be attributable to adverse weather conditions," said Gennadiy Goldberg, an economist at TD Securities in New York. The Philadelphia Fed index came on the heels of a report on Tuesday that showed a sharp cooling in factory activity in New York State in February. But a survey of national factory activity also released on Thursday indicated manufacturing activity grew in February at its fastest pace in nearly four years. Financial data firm Markit said its "flash" or preliminary U.S. Manufacturing Purchasing Managers Index rose to 56.7 in February, its highest level since May 2010, from 53.7 in January. Readings above 50 indicate expansion. "This suggests that the regional Federal Reserve indicators may be overstating the extent of manufacturing weakness during the month," said Goldberg. INFLATION SUBDUED DESPITE HEATING SPIKE The cold weather is also putting a strain on household budgets. In another report, the Labor Department said strong gains in the price of household energy had accounted for most of the 0.1 percent rise in its Consumer Price Index in January. The CPI had advanced 0.2 percent in December. In January, electricity prices rose 1.8 percent, the largest gain since March 2010. Natural gas prices surged 3.6 percent. That was the largest rise since April. The cost of heating oil jumped 3.7 percent, the biggest increase since September 2012. The increases, which offset a 1.0 percent fall in the price of gasoline, come against the backdrop of subdued income growth. Average weekly earnings adjusted for inflation rose 0.1 percent in January after sliding 0.5 percent in December. "Higher energy prices could take a toll on consumer spending this winter," said Jay Morelock, an economist at FTN Financial in New York. "The jump in energy prices should subside once shortages of fuel oil and propane are alleviated," he added. Propane stocks are well below average levels for this time of year, while total stocks of natural gas in underground storage are 40 percent lower than a year ago. Overall, the data showed inflation remained contained. Stripping out the volatile energy and food components, the so-called core CPI also rose 0.1 percent in January for a second straight month. Consumer prices advanced 1.6 percent in the 12 months to January, after increasing 1.5 percent in December. Core CPI rose 1.6 percent on the year, slowing from a 1.7 percent increase in December and the smallest rise since June. With inflation continuing to run below the Federal Reserve's 2 percent target, the central bank is likely to keep interest rates low for some time to boost growth, even as it reduces the amount of money it is injecting into the economy each month through bond purchases. "There is no rush to raise the federal funds rate. They will continue to taper (bond buys) unless the weakness we have seen in the last couple of months doesn't reverse itself as soon as the weather gets better," said Navy Federal Credit Union's MacEachin.