* Front month remains above recent 3-month low * Forecasters predict long-term milder weather * Nuclear outages running above normal levels By Eileen Houlihan NEW YORK, Feb 5 (Reuters) - U.S. natural gas futures rose early Monday, lifted by near-term cold weather in the eastern half of the country that has boosted heating demand. But with milder weather on tap in longer-term outlooks and still bloated inventories, most traders expect limited upside. As of 9:16 a.m. EST (1416 GMT), front-month March natural gas futures on the New York Mercantile Exchange were at $3.332 per million British thermal units, up 1.7 cents, or less than 1 percent. The front month contract hit a 6-1/2-week high of $3.645 two weeks ago after hitting a more than three-month low of $3.05 in early January. The latest National Weather Service six to 10-day forecast issued on Monday again called for above-normal readings for about the eastern half of the United States, with below-normal temperatures across the West and some normal readings in the mid-Continent. Nuclear outages totaled 8,500 megawatts, or 8 percent of U.S. capacity, flat to Monday's outages, up from 7,900 MW out a year-ago, but below the five-year average outage rate of about 10,600 MW. STORAGE DRAW FALLS SHORT OF EXPECTATIONS Last week's storage report from the U.S. Energy Information Administration showed domestic gas inventories fell the prior week by 194 billion cubic feet, below industry expectations for a 206-bcf draw. Most traders viewed the decline as bearish, noting it was below market expectations for the first time in five weeks. But others noted the draw was above the year-ago drop of 149 bcf and the five-year average draw of 178 bcf. Storage now stands 202 bcf, or about 7 percent, below last year's record high levels, but 304 bcf, or more than 12 percent, above the five year-average. Early withdrawal estimates for this week's inventory report range from 126 bcf to 162 bcf, well above the 94 bcf pulled from storage during the same week in 2012, but in line with the five-year average decline for that week of 165 bcf. If drawdowns for the rest of winter match the five-year average, inventories will end March at 2.032 tcf, about 18 percent above normal but 18 percent below last year, when stocks finished a very mild heating season at a record-high 2.48 tcf. GAS RIG COUNT FALLS, OUTPUT STILL NEAR RECORD Baker Hughes data last week showed the gas-directed drilling rig count fell for the third time in four weeks, dropping by six to 428. While the gas rig count is hovering not far above the 13-1/2-year low of 413 hit about three months ago, production has shown no significant sign of slowing. EIA estimates that marketed gas output in 2013 will hit a record high for the third straight year.