Month select in UI component form

Actually i don't think so magento give default functionality to drop down select month, but you can archive this by custom way

Step 1 : add below code in your UI Component file

<column name="months">
<argument name="data" xsi:type="array">
    <item name="options" xsi:type="object">Namespace\Your_Module\Model\Source\Months</item>
    <item name="config" xsi:type="array">
        <item name="filter" xsi:type="string">select</item>
        <item name="component" xsi:type="string">Magento_Ui/js/grid/columns/select</item>
        <item name="editor" xsi:type="string">select</item>
        <item name="dataType" xsi:type="string">select</item>
        <item name="label" xsi:type="string" translate="true">Months</item>
        <item name="sortOrder" xsi:type="number">60</item>
    </item>
</argument>

Step 2 : Create a source model under Namespace\Your_Module\Model\Source

Months.php

<?php
namespace Namespace\ModuleName\Model\Source;

use Magento\Framework\Data\OptionSourceInterface;

/**
* Class Status
*/
class Months implements OptionSourceInterface
{
/**
 * Get the options
 *
 * @return array
 */
public function toOptionArray()
{
    return [
        ['label' => __('January'), 'value' => '0'],
        ['label' => __('February'), 'value' => '1'],
        ['label' => __('March'), 'value' => '2'],
        ['label' => __('April'), 'value' => '3'],
        ['label' => __('May'), 'value' => '4'],
        ['label' => __('June'), 'value' => '5'],
        ['label' => __('July'), 'value' => '6'],
        ['label' => __('August'), 'value' => '7'],
        ['label' => __('September'), 'value' => '8'],
        ['label' => __('October'), 'value' => '9'],
        ['label' => __('November'), 'value' => '10'],
        ['label' => __('December'), 'value' => '11']
    ];
}
}