* Gas rig count down 4 to 421 * Oil rig count up, horizontal rigs fall NEW YORK, Feb 15 The number of rigs drilling for natural gas in the United States fell this week as low gas prices continued to slow drilling activity, data from Houston-based oil services firm Baker Hughes Inc showed on Friday. The gas-directed rig count dropped by four to 421, the fifth fall in six weeks, according to Baker Hughes. The gas count has fallen near to levels not seen for over 13 years, as producers curb dry-gas drilling in favor of more profitable oil and liquids-rich plays. The oil-focused rig count rose by 7 to 1,337, Baker Hughes data showed. The oil count is up 65 rigs from the same week last year. Baker Hughes also reported that horizontal rigs, the type often used to extract oil or gas from shale, fell 4 this week to 1,139. The horizontal count, which has risen in seven of the last ten weeks, is still down about 4 percent from the record high of 1,193 set in May. Drilling for natural gas has mostly been in decline for more than a year - the count is down about 55 percent since peaking in 2011 at 936 - but so far production has not shown any significant signs of slowing. The associated gas produced from more-profitable shale oil and shale gas liquids wells has kept dry gas flowing at, or near, a record pace. U.S. Energy Information Administration data showed that November gross natural gas production in the lower 48 U.S. states rose to a record high for a third straight month.