* Front month hits more than five-week high * Cold weather on tap in long-term outlooks * Nuclear outages still running above normal By Eileen Houlihan NEW YORK, March 5 (Reuters) - U.S. natural gas futures edged higher for a second straight day on Tuesday, lifted to a near six-week high by forecasts for continued cold weather for most of the nation despite bloated inventories. As of 9:22 a.m. EST (1422 GMT), front-month April natural gas futures on the New York Mercantile Exchange were at $3.572 per million British thermal units, up 4.3 cents, or more than 1 percent, after climbing more than 2 percent on Monday to $3.529. It was the first front-month close above $3.50 in six weeks, and could set the stage for more upside, but most technical traders would like to see a close above the 2013 high of $3.645 posted in late January to turn more bullish. Forecaster MDA Weather Services called for normal or below-normal readings across the country in its one to five-day outlook, with much of the cold concentrated in the South and the West. The latest National Weather Service six to 10-day forecast issued on Monday called for below-normal temperatures for the mid-Continent and normal or above-normal readings on both coasts. Nuclear outages totaled about 15,300 megawatts, or 15 percent of U.S. capacity, down slightly from 15,800 MW on Monday and 19,300 MW a year-ago, but up from a five-year average outage rate of about 13,500 MW. ABOVE-AVERAGE STORAGE DRAW U.S. Energy Information Administration data last week showed domestic gas inventories fell the prior week by 171 billion cubic feet to 2.229 trillion cubic feet. The weekly draw came in well above the five-year average drop for that week and storage is now 12 percent below last year's record high levels, but it is also 16 percent above the five-year average level. Withdrawal estimates for this week's storage report range from 120 bcf to 160 bcf versus a 92 bcf draw in the same week in 2012 and a five-year average drop for that week of 107 bcf. Most analysts expect storage to end the heating season at about 2 tcf, or 16 percent above average, but 19 percent below last winter's record-high finish of 2.48 tcf. OUTPUT COULD BE STARTING TO SLOW Baker Hughes data on Friday showed the gas-directed drilling rig count fell for the fourth time in five weeks, dropping by eight to 420. The gas drilling rig count is hovering just above the 13-1/2-year low of 413 hit in early November, but production is still high. EIA data last week showed that gross natural gas output in December slipped slightly from November's record high, the first time in four months that production failed to set a new peak. But most analysts pegged the decline to cold weather in the Southwest that likely froze wells and not producers intentionally curbing dry gas flows. The EIA expects marketed gas production in 2013 to hit a record high for the third straight year.