* Cold forecasts, particularly for Midwest, support prices * Front futures hit highest since late July 2011 By Joe Silha NEW YORK, April 12 (Reuters) - U.S. natural gas futures ended higher on Friday for a third straight day, with cold Midwest weather forecasts for the next week and the recent slide in inventories to below-normal levels driving the front contract to a new 20-month high. Traders said persistent late-winter cold, particularly in the Midcontinent region, has helped drive the front-month contract up about 35 percent over the last two months. Some traders also viewed Thursday's 14 billion cubic feet weekly inventory draw as supportive for prices, noting stocks typically build slightly during that week. The U.S. Energy Information Administration report showed that total domestic gas inventories fell last week to 1.673 trillion cubic feet, 32 percent below last year's record highs for that time and 4 percent below average. The sharp drop in stored gas over the last two months, also driven by above-average nuclear plant outages, helped tighten supplies and prompted some analysts to raise price expectations for this year. Front-month gas futures on the New York Mercantile Exchange ended up 8.3 cents, or 2 percent, at $4.222 per million British thermal units after notching a 20-month high of $4.249. Nearby futures gained 5.1 percent in the last three sessions. Despite modest losses early in the week, the front contract ended the week up 2.4 percent, the eighth straight weekly rise. "The market looks like it has further upside to go. The weather looks pretty supportive, and that should keep April storage builds low," said Steve Mosley at The SMC Report. Some traders remain skeptical of the upside, noting production was still flowing at robust levels and space heating needs were likely to slow once milder spring weather arrives. They also note that gas prices are nearing levels that could tempt producers to increase supplies by turning on more wells. Forecaster MDA Weather Services still expects temperatures in the Midwest to average below normal for the next two weeks, while readings in the South and East will mostly range from seasonal to above seasonal levels. INJECTION SEASON SET TO KICK OFF Thursday's inventory drawdown should be the last of the heating season, with estimates for next week's report looking for a modest build. Early injection estimates for that report range from 16 to 55 bcf versus a 21-bcf build during the same week last year and a five-year average rise for that week of 39 bcf. Total gas pulled from storage this winter was about 2.25 tcf, roughly 770 bcf, or 52 percent more than last year and 15 percent more than the normal draw during the heating season. RIG COUNT CLIMBS, WHEN WILL OUTPUT SLOW? Baker Hughes data on Friday showed the gas-directed rig count rose this week by two to 377, stirring concerns that higher gas prices may be stirring more dry gas drilling. The gas rig count posted a 14-year low last week. Drilling for natural gas has mostly been in decline for the last 18 months. The count is down about 60 percent since peaking in 2011 at 936, but so far production has not slowed much from the record high hit last year. In its short-term energy outlook on Tuesday, EIA trimmed its estimate for domestic gas production growth in 2013 but still expects output to rise 0.3 percent from 2012's record levels.