may be this is what you looking for
you need to set padding to second td or th
.search-table tr th:nth-child(2), .search-table tr td:nth-child(2) {
    padding-left: 100px;
}
body {
    color: white;
}
.search-table-outter {
    width: auto; 
    max-width: 735px;
    margin-left: 5em;
    margin-right: auto;
    padding-top: 30px;
}
.search-table{
    table-layout: fixed; 
    margin:0px auto 0px auto; 
    background-color: lightblue
}
.search-table, td, th{
    border-collapse:collapse; 
    border-bottom:1px solid white;
    line-height: 10px;
}
th{
    padding:5px 7px; 
    font-size:15px; 
}
td{
    padding:5px 10px; 
    height:35px;
}
.search-table-outter { overflow-x: scroll; }
th, td { min-width: 100px; }
.headcol {
    position: absolute;
    color: black;
    left: auto;
    width: 5em;
    top: auto;
}
.search-table tr th:nth-child(2), .search-table tr td:nth-child(2) {
    padding-left: 100px;
}
<div class="container header">
<div class="search-table-outter wrapper">
  <table class="search-table inner">
    <tr>
      <th class="headcol">Time</th>
      <th>Icon</th>
      <th>Description</th>
      <th>Temp</th>
      <th>Precip</th>
      <th>Wind</th>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
    <tr>
      <td class="headcol">4:11 </td> 
      <td>Cloud </td>
      <td>Partly Cloudy </td>
      <td>86 </td>
      <td>0% </td>
      <td>8.38 mph </td>
    </tr>
  </table>
</div>
</div>
 
 
see fiddle https://jsfiddle.net/s8bczc0L/